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Wamakelekile kwintetho echaza indlela yokusebenzisa i"quadratic equation".
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Ngoko ke i"quadratic equation". ivakala ngathi yinto
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enobunzima kakhulu.
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Kwaye xa uqala ukubona i"quadratic equation, ungathi
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kulungile, hayi ukuphela ivakala njengento
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enobunzima, kodwa yinto enzima.
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Kodwa ngethemba uakubona, njengokuba sisaqubekeka
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nentetho yethu, ukuba ayikhonzima ukuyisebenzisa.
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Kwaye kwintetho ezayo exesheni ndizakubonisa
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indlela eyakhiwe ngayo.
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Ngoko ke, jikelele, sowufundile ukwenza ucalu calulo
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kwiqondo lesibini lalonxaki.
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Ufundile ukuba, ukuba ndino, mandithi "x" ophinda-phindwe kabini thabatha
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"x" thabatha 6, ilingana no0.
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Ukuba bendinalenxaki. "x" ophinda-phindwe kabini thabatha "x" thabtha "x' ilingana
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no0, lanto ungayicalu calulala uthi "x" thabatha 3 kwaye
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"x" dibanisa 2 ilingana no0.
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Ngokucacileyo ithetha ukuba "x" thabatha 3 lingana no 0 okanye
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"x" dibanis 2 lingana no0.
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Ngoko ke "x" thabatha 3 lingana no0 okanye "x' dibanisa 2 lingana no0.
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Ngoko ke "x" lingana no 3 okanye no thabatha 2.
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Kwaye, xa siyizoba phantsi yalento izakuba, ukuba bendino
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msebenzi othile "f" ka "x" ulingana no "x" ophinda-phindwe kabnini thabatha "x' thabatha 6.
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Ngoko ke lomgca usembindini ngoka "f" ka "x".
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Ungaqhelana kakhulu nomgca osembindini we"y".
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kulenxaki inje, akukho nxaki khakhulu.
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Kwaye lomgca usembindini we "x".
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Kwaye ukuba bekuzakufuneka ndiyizobile lenxaki, "x' ophinda-phindwe kabini thabatha "x"
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thabatha 6, ingajongeka ngoluhlobo.
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Kancinci ngoluhlobo--lento ngu "f' ka "x" ulingana no thabatha 6.
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Kwaye umfanekiso ozotyiweyo angakhangeleka ngolu hlobo.
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Nyuka, izakuhlala inyuka ngokwalandlela.
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Kwaye ngoku iya kuthabatha 6, ngoba xa "x' elingana no0.
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'F" ka 'x" ulingana no thabatha 6.
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Ngoko ke ndiyayazi iyagqitha pha kulancam.
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kwaye ndiyayazi ukuba xa "f' ka 'x' elingana no0, ngoko ke 'f' ka 'x' lingana
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no 0 ngaphezu komgca osembindini ka 'x', akunjalo?
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Ngoba lento ngu1.
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lento ngu0.
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lento ngu thabatha 1.
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Ngoko ke lento ngu, xa 'f' ka 'x' elingana no0, ngaphezulu
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komgca osembindini ka 'x', akunjalo?
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Kwaye siyayazi ilingana no0 kula ncam 'x' lingana no 3 kwaye
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'x' lingana no thabatha 2.
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Yeyonanto isiyicombululeyo apha.
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Mhlawumbi xeshikweni besisenza inxaki yokucazulula khange
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siqwalasele ngokomzobo wethu into besiyenza.
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Kodwa ukuba sithi la 'f' ka 'x' ulingana nenaki ethile, sayi
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lungiselela lanto yalingana no0.
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Ngoko ke sithi lenxaki, kuphi apho
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ilingana no0?
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Xa kutheni ilingana no0?
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Kulungile, ilingana no0 kwincam, akunjalo/
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Ngoba kulapho u'f' ka 'x' elingana no0.
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Kwaye kwangoko into besiyenza xa besisombulula lento ngoku
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cazulula ku, sibonile ukuba, iinxnye zika'x' ezenze u 'f' ka 'x'
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lingana no0, ngokucacileyo ngezi ncam zimbini.
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Kwaye, ngokwe sigama, ezi zibizwa
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ngamaqanda, okanye ingcambu, zika 'f' ka 'x'.
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Makhe siqwalase lanto kancinane.
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Ngoko ke , ukuba ndinento enje ngo'f' ka 'x' ulingana no'x' ophinda-phindwe kabini dibanisa
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'4x' dibanisa 4, kwaye ndibuze kuwe, aphi amaqanda okanye
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ingcambu zika 'f' ka'x'.
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Yinto enye nokuthi, kuphi apho u'f' ka 'x'
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adinana khona nomngca osembindini ka'x'.
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Kwaye badibana xa umgca osembindika ka'x' 'f' ka 'x' eli
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ngana no0, akunjalo?
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Ukuba uyacinga ngomzobo bendikhe ndawenza we'graph'.
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Ngoko ke, masithi ukuba u 'x' ulingana no 0, kwangoko
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singathi, 0 ulingana no'x' ophinda-phindwe kabini dibanisa '4x' dibanisa 4.
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Kwaye siyayazi, singazicalu calula, ngu 'x'
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dibanisa 2 phinda-phinda 'x' dibanisa 2.
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Kwaye siyayazi ukuba iyalingana no0 xa 'x' elingana no thabatha 2.
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'x' ulingana no thabatha 2.
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Kulungile, kancinci--'x' ulingana no thabatha 2.
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Ngoko ke ngoku, siyayazi singamfumana njani u0 xa eyona
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nxaki kulula ukuyicazulula.
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Kodwa masenze eyona nxaki apho inxaki yethu
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kungakho lula ukuyicazulula konke konke.
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Masithi sino 'f' ka 'x' ulingana nothabatha '10x'
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ophinda-phindiweyo kabini thabatha '9x' dibanisa 1.
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Kulungile, xa ndijonga lento, nokuba bendino kuyahlula ngo 10 bendino
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nokufumana amaqhezu apha.
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Kwaye kunzima ukuyicinga indlela yokucazulula lento i'quadratic'
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Kwaye yilonto ibizwa ngokuba yi"quadratic equation" okanye
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liqondo lesibini lamanani anezalathi ezinga phezu kwesithathu.
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Kodwa masiyicwangcise-- Ngoko ke sizama ukuyisombulula lento.
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Ngoba sifuna ukuyazi kuphi xa ilingana no0.
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Thaba '10x' ophonda-phindwe kabini thabatha '9x' dibanisa 1.
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Sifuna ukwazi ngawaphi lamanani asendaweni ka'x' enza lento
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ilingane no0.
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Kwaye apha singasebenzisa isixhobo esibizwa ngokuba yi"quadratic equation".
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Kwaye ngoku ndizakuninika enye kezinqabileyo kwizibalo
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kwaye ngumbono omhle ukuyigcina enqondweni.
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I"quadratic equation' ithi ingcambu ze"quadratic'
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ziyalingana--kwaye masithi i'quadratic equation' ngu
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'x' mophinda-phindwe kabini dibanisa 'bx' dibanisa 'c' lingana no0.
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Ngoko ke kulomzekelo, u'a' ngu thabatha 10.
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'b' ngu thabatha 9, kwaye 'c' ngu 1.
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Isichazi se"quadratic fomula' yi ngcambu ka 'x' ilingana no thabatha 'b' dibanisa okanye thabatha
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ingcambu ephinda-phindwa kabini ka'b' thabatha u 4 phinda-phinda 'a' phinda-phinda 'c',
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yonke lonto ngaphezu ko' 2a'.
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Ndiyayazi ukuba ijongenga nzima kodwa xa uyisebenzisa ngamandla, uzakubona
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ukuba ayikhombi kwaphela.
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Kwaye ngumbono omhle ukuyi bamba ngengqondo.
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Ngoko ke masibandakanye i"quadratic ewauation' apha kulenxaki
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sisandula ukuyibhala phantsi.
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Ngoko ke ndithi sandula ukuthi--kwaye jonga, kukho into ecaleni
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kuka 'x', akunjalo?
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'a' ngumlingani ka 'x' ophinda-phindiweyo.
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'b' ngumlingani ka 'x' kwaye u'c' akatshintshi.
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Ngoko ke masiyisebenzise kule nxaki.
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Ngubani u-'b'?
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Kulungile, 'b' ngu thabatha 9.
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Singabona apha.
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'b' nguthabatha 9, 'a' ngu thabatha 10.
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'c' ngu 1.
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Akunjalo?
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Ngoko ke ukuba u-'b' ngu thabatha 9--ngoko ke masithi, nguthabatha 9.
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Dibanisa okanye thabatha ingcambu kathabatha 9 ophinda-phindwe kabini.
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Kulungile, ngu 81.
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thabatha 4 phinda-phinda ngo 'a'
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'a' ngu thabatha 10.
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Thabatha 10 phinda-phinda 'c', ngokucacileyo ngu 1.
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Ndiyayazi lento ithesa, kodwa ngethemba uza
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kuyiqonda.
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kwaye yonke lonto ngaphezu ko2 umphinda-phinde ngo 'a'.
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Kulungile, 'a' ngu thabatha 10, ngoko ke 2 phinda-phinda 'a' ngu thabahta 20.
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Ngoko ke masiyicazulule lanto.
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Thabatha 10 phinda-phinda ngo thabatha 6, ngu dibanisa 9.
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Dibanisa okanye thabatha ingcambu ka 81.
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Sino thabatha 4 umphinda-phinda ngo thabatha 10.
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Lento ngu thabatha 10.
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Ndiyayazi ithesa kakhulu, ndiyaxolisa kakhulu
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ngalonto, phinda-phinda ngo 1.
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ngoko ke thabatha 4 uphinda-phinde ngo thabatha 10 ngu 40, onesichazi esingu dibanisa 40.
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Dibanisa 40.
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Kwaye kwangoko sinazo zonke phezu ko thabatha 20.
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Kulungile, 81 dibanisa 40 ngu 121.
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Ngoko ke lento ngu 9 dibanisa okanye thabatha ingcambu
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ka 121 phezu ko thabatha 20.
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Ingcambu ka 121 ngu 11.
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Ngoko ke ndizohamba apha.
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Ngethemba awuzose uyiphose indlela yalento ndiyenzayo.
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Ngoko ke lento ngu 9 dibanisa oakanye thabatha 11, ngaphezu ko thabatha 20.
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kwaye ngoko ke ukuba sithi 9 dibanisa 11 phezu ko thabatha 20, ngu 9
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dibanisa 11 ngu 20, ngoko ke lenti ngu 20 phezu ko thabatha 20.
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Ngoku cacileyo ulingana no thabatha 1.
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Ngoko ke yigcambu enye.
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Ngu 9 dibanisa--ngoba lento ngu dibanisa oaknye thabatha.
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Kwaye enye ingcambu izakuba ngu 9 thabatha 11 phezu ko thabatha 20.
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Ngokucacileyo ilingana no thabatha 2 phezu ko thabatha 20.
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ngokucacileyo ilingana no 1 phezu ko 10.
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ngoko ke ngenye ingcambu.
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Ngoko ke ukuba bekunokufuneka ziyizobe phantsi lenxaki, besizokubona ukuba
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ngokucacileyo idibana kumgca osembindini ka'x',
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Okanye 'f' ka 'x' ulingana no0 kwincam ka'x' elingana no thabatha
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1 kwaye 'x' ulingana no 1/10.
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Ndizakwenza imizekelo eminizni kwicandelo lesibini, ngoba ndi
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yacinga, ukuba nantoni na, ndingani bhidekisa
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ngalena yodwa.
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ngoko ke, ndizakunibona kwicandelo lesibini sisebenzisa
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"quadratic equation".