0:00:01.010,0:00:04.520
Wamakelekile kwintetho echaza indlela yokusebenzisa i"quadratic equation".

0:00:04.520,0:00:06.730
Ngoko ke i"quadratic equation". ivakala ngathi yinto

0:00:06.730,0:00:07.810
enobunzima kakhulu.

0:00:07.810,0:00:09.930
Kwaye xa uqala ukubona i"quadratic equation, ungathi

0:00:09.930,0:00:11.590
kulungile, hayi ukuphela ivakala njengento

0:00:11.590,0:00:13.110
enobunzima, kodwa yinto enzima.

0:00:13.110,0:00:14.930
Kodwa ngethemba uakubona, njengokuba sisaqubekeka

0:00:14.930,0:00:16.580
nentetho yethu, ukuba ayikhonzima ukuyisebenzisa.

0:00:16.580,0:00:19.040
Kwaye kwintetho ezayo exesheni ndizakubonisa

0:00:19.040,0:00:21.300
indlela eyakhiwe ngayo.

0:00:21.300,0:00:24.810
Ngoko ke, jikelele, sowufundile ukwenza ucalu calulo

0:00:24.810,0:00:25.810
kwiqondo lesibini lalonxaki.

0:00:25.810,0:00:30.910
Ufundile ukuba, ukuba ndino, mandithi "x" ophinda-phindwe kabini thabatha

0:00:30.910,0:00:40.340
"x" thabatha 6, ilingana no0.

0:00:40.340,0:00:42.970
Ukuba bendinalenxaki. "x" ophinda-phindwe kabini thabatha "x" thabtha "x' ilingana

0:00:42.970,0:00:48.720
no0, lanto ungayicalu calulala uthi "x" thabatha 3 kwaye

0:00:48.720,0:00:52.210
"x" dibanisa 2 ilingana no0.

0:00:52.210,0:00:54.955
Ngokucacileyo ithetha ukuba "x" thabatha 3 lingana no 0 okanye

0:00:54.955,0:00:57.073
"x" dibanis 2 lingana no0.

0:00:57.073,0:01:03.512
Ngoko ke "x" thabatha 3 lingana no0 okanye "x' dibanisa 2 lingana no0.

0:01:03.512,0:01:08.500
Ngoko ke "x" lingana no 3 okanye no thabatha 2.

0:01:08.500,0:01:17.980
Kwaye, xa siyizoba phantsi yalento izakuba, ukuba bendino

0:01:17.980,0:01:26.150
msebenzi othile "f" ka "x" ulingana no "x" ophinda-phindwe kabnini thabatha "x' thabatha 6.

0:01:26.150,0:01:28.760
Ngoko ke lomgca usembindini ngoka "f" ka "x".

0:01:28.760,0:01:32.670
Ungaqhelana kakhulu nomgca osembindini we"y".

0:01:32.670,0:01:34.780
kulenxaki inje, akukho nxaki khakhulu.

0:01:34.780,0:01:36.270
Kwaye lomgca usembindini we "x".

0:01:36.270,0:01:40.430
Kwaye ukuba bekuzakufuneka ndiyizobile lenxaki, "x' ophinda-phindwe kabini thabatha "x"

0:01:40.430,0:01:42.380
thabatha 6, ingajongeka ngoluhlobo.

0:01:42.380,0:01:50.130
Kancinci ngoluhlobo--lento ngu "f' ka "x" ulingana no thabatha 6.

0:01:50.130,0:01:52.900
Kwaye umfanekiso ozotyiweyo angakhangeleka ngolu hlobo.

0:01:52.900,0:01:57.150
Nyuka, izakuhlala inyuka ngokwalandlela.

0:02:00.030,0:02:03.150
Kwaye ngoku iya kuthabatha 6, ngoba xa "x' elingana no0.

0:02:03.150,0:02:05.110
'F" ka 'x" ulingana no thabatha 6.

0:02:05.110,0:02:07.800
Ngoko ke ndiyayazi iyagqitha pha kulancam.

0:02:07.800,0:02:11.520
kwaye ndiyayazi ukuba xa "f' ka 'x' elingana no0, ngoko ke 'f' ka 'x' lingana

0:02:11.520,0:02:14.960
no 0 ngaphezu komgca osembindini ka 'x', akunjalo?

0:02:14.960,0:02:16.600
Ngoba lento ngu1.

0:02:16.600,0:02:17.870
lento ngu0.

0:02:17.870,0:02:19.160
lento ngu thabatha 1.

0:02:19.160,0:02:21.510
Ngoko ke lento ngu, xa 'f' ka 'x' elingana no0, ngaphezulu

0:02:21.510,0:02:23.420
komgca osembindini ka 'x', akunjalo?

0:02:23.420,0:02:29.210
Kwaye siyayazi ilingana no0 kula ncam 'x' lingana no 3 kwaye

0:02:29.210,0:02:32.330
'x' lingana no thabatha 2.

0:02:32.330,0:02:34.360
Yeyonanto isiyicombululeyo apha.

0:02:34.360,0:02:36.440
Mhlawumbi xeshikweni besisenza inxaki yokucazulula khange

0:02:36.440,0:02:38.940
siqwalasele ngokomzobo wethu into besiyenza.

0:02:38.940,0:02:42.070
Kodwa ukuba sithi la 'f' ka 'x' ulingana nenaki ethile, sayi

0:02:42.070,0:02:43.270
lungiselela lanto yalingana no0.

0:02:43.270,0:02:44.820
Ngoko ke sithi lenxaki, kuphi apho

0:02:44.820,0:02:48.220
ilingana no0?

0:02:48.220,0:02:49.390
Xa kutheni ilingana no0?

0:02:49.390,0:02:51.720
Kulungile, ilingana no0 kwincam, akunjalo/

0:02:51.720,0:02:55.360
Ngoba kulapho u'f' ka 'x' elingana no0.

0:02:55.360,0:02:57.490
Kwaye kwangoko into besiyenza xa besisombulula lento ngoku

0:02:57.490,0:03:01.970
cazulula ku, sibonile ukuba, iinxnye zika'x' ezenze u 'f' ka 'x'

0:03:01.970,0:03:04.160
lingana no0, ngokucacileyo ngezi ncam zimbini.

0:03:04.160,0:03:06.740
Kwaye, ngokwe sigama, ezi zibizwa

0:03:06.740,0:03:09.860
ngamaqanda, okanye ingcambu, zika 'f' ka 'x'.

0:03:09.860,0:03:12.470
Makhe siqwalase lanto kancinane.

0:03:14.810,0:03:23.700
Ngoko ke , ukuba ndinento enje ngo'f' ka 'x' ulingana no'x' ophinda-phindwe kabini dibanisa

0:03:23.700,0:03:29.550
'4x' dibanisa 4, kwaye ndibuze kuwe, aphi amaqanda okanye

0:03:29.550,0:03:31.770
ingcambu zika 'f' ka'x'.

0:03:31.770,0:03:33.970
Yinto enye nokuthi, kuphi apho u'f' ka 'x'

0:03:33.970,0:03:36.300
adinana khona nomngca osembindini ka'x'.

0:03:36.300,0:03:38.210
Kwaye badibana xa umgca osembindika ka'x' 'f' ka 'x' eli

0:03:38.210,0:03:39.440
ngana no0, akunjalo?

0:03:39.440,0:03:42.120
Ukuba uyacinga ngomzobo bendikhe ndawenza we'graph'.

0:03:42.120,0:03:45.720
Ngoko ke, masithi ukuba u 'x' ulingana no 0, kwangoko

0:03:45.720,0:03:51.860
singathi, 0 ulingana no'x' ophinda-phindwe kabini dibanisa '4x' dibanisa 4.

0:03:51.860,0:03:53.940
Kwaye siyayazi, singazicalu calula, ngu 'x'

0:03:53.940,0:03:57.080
dibanisa 2 phinda-phinda 'x' dibanisa 2.

0:03:57.080,0:04:07.090
Kwaye siyayazi ukuba iyalingana no0 xa 'x' elingana no thabatha 2.

0:04:07.090,0:04:10.170
'x' ulingana no thabatha 2.

0:04:13.940,0:04:18.270
Kulungile, kancinci--'x' ulingana no thabatha 2.

0:04:18.270,0:04:22.380
Ngoko ke ngoku, siyayazi singamfumana njani u0 xa eyona

0:04:22.380,0:04:24.560
nxaki kulula ukuyicazulula.

0:04:24.560,0:04:27.500
Kodwa masenze eyona nxaki apho inxaki yethu

0:04:27.500,0:04:28.850
kungakho lula ukuyicazulula konke konke.

0:04:28.850,0:04:32.120
Masithi sino 'f' ka 'x' ulingana nothabatha '10x'

0:04:39.750,0:04:45.380
ophinda-phindiweyo kabini thabatha '9x' dibanisa 1.

0:04:45.380,0:04:47.580
Kulungile, xa ndijonga lento, nokuba bendino kuyahlula ngo 10 bendino

0:04:47.580,0:04:48.650
nokufumana amaqhezu apha.

0:04:48.650,0:04:53.130
Kwaye kunzima ukuyicinga indlela yokucazulula lento i'quadratic'

0:04:53.130,0:04:54.860
Kwaye yilonto ibizwa ngokuba yi"quadratic equation" okanye

0:04:54.860,0:04:57.580
liqondo lesibini lamanani anezalathi ezinga phezu kwesithathu.

0:04:57.580,0:04:59.600
Kodwa masiyicwangcise-- Ngoko ke sizama ukuyisombulula lento.

0:04:59.600,0:05:02.420
Ngoba sifuna ukuyazi kuphi xa ilingana no0.

0:05:02.420,0:05:07.130
Thaba '10x' ophonda-phindwe kabini thabatha '9x' dibanisa 1.

0:05:07.130,0:05:09.090
Sifuna ukwazi ngawaphi lamanani asendaweni ka'x' enza lento

0:05:09.090,0:05:11.260
ilingane no0.

0:05:11.260,0:05:13.730
Kwaye apha singasebenzisa isixhobo esibizwa ngokuba yi"quadratic equation".

0:05:13.730,0:05:15.625
Kwaye ngoku ndizakuninika enye kezinqabileyo kwizibalo

0:05:15.625,0:05:18.030
kwaye ngumbono omhle ukuyigcina enqondweni.

0:05:18.030,0:05:21.330
I"quadratic equation' ithi ingcambu ze"quadratic'

0:05:21.330,0:05:24.810
ziyalingana--kwaye masithi i'quadratic equation' ngu

0:05:24.810,0:05:31.900
'x' mophinda-phindwe kabini dibanisa 'bx' dibanisa 'c' lingana no0.

0:05:31.900,0:05:35.790
Ngoko ke kulomzekelo, u'a' ngu thabatha 10.

0:05:35.790,0:05:39.940
'b' ngu thabatha 9, kwaye 'c' ngu 1.

0:05:39.940,0:05:48.040
Isichazi se"quadratic fomula' yi ngcambu ka 'x' ilingana no thabatha 'b' dibanisa okanye thabatha

0:05:48.040,0:05:58.060
ingcambu ephinda-phindwa kabini ka'b' thabatha u 4 phinda-phinda 'a' phinda-phinda 'c',

0:05:58.060,0:06:00.230
yonke lonto ngaphezu ko' 2a'.

0:06:00.230,0:06:02.843
Ndiyayazi ukuba ijongenga nzima kodwa xa uyisebenzisa ngamandla, uzakubona

0:06:02.843,0:06:04.400
ukuba ayikhombi kwaphela.

0:06:04.400,0:06:07.720
Kwaye ngumbono omhle ukuyi bamba ngengqondo.

0:06:07.720,0:06:10.730
Ngoko ke masibandakanye i"quadratic ewauation' apha kulenxaki

0:06:10.730,0:06:12.670
sisandula ukuyibhala phantsi.

0:06:12.670,0:06:15.260
Ngoko ke ndithi sandula ukuthi--kwaye jonga, kukho into ecaleni

0:06:15.260,0:06:18.610
kuka 'x', akunjalo?

0:06:18.610,0:06:20.300
'a' ngumlingani ka 'x' ophinda-phindiweyo.

0:06:20.300,0:06:23.570
'b' ngumlingani ka 'x' kwaye u'c' akatshintshi.

0:06:23.570,0:06:25.100
Ngoko ke masiyisebenzise kule nxaki.

0:06:25.100,0:06:26.250
Ngubani u-'b'?

0:06:26.250,0:06:28.700
Kulungile, 'b' ngu thabatha 9.

0:06:28.700,0:06:29.970
Singabona apha.

0:06:29.970,0:06:33.980
'b' nguthabatha 9, 'a' ngu thabatha 10.

0:06:33.980,0:06:34.970
'c' ngu 1.

0:06:34.970,0:06:36.090
Akunjalo?

0:06:36.090,0:06:42.350
Ngoko ke ukuba u-'b' ngu thabatha 9--ngoko ke masithi, nguthabatha 9.

0:06:42.350,0:06:49.260
Dibanisa okanye thabatha ingcambu kathabatha 9 ophinda-phindwe kabini.

0:06:49.260,0:06:49.810
Kulungile, ngu 81.

0:06:49.810,0:06:53.140
thabatha 4 phinda-phinda ngo 'a'

0:06:56.940,0:06:59.760
'a' ngu thabatha 10.

0:06:59.760,0:07:03.240
Thabatha 10 phinda-phinda 'c', ngokucacileyo ngu 1.

0:07:03.240,0:07:05.110
Ndiyayazi lento ithesa, kodwa ngethemba uza

0:07:05.110,0:07:06.470
kuyiqonda.

0:07:06.470,0:07:09.560
kwaye yonke lonto ngaphezu ko2 umphinda-phinde ngo 'a'.

0:07:09.560,0:07:14.050
Kulungile, 'a' ngu thabatha 10, ngoko ke 2 phinda-phinda 'a' ngu thabahta 20.

0:07:14.050,0:07:14.990
Ngoko ke masiyicazulule lanto.

0:07:14.990,0:07:19.410
Thabatha 10 phinda-phinda ngo thabatha 6, ngu dibanisa 9.

0:07:19.410,0:07:26.460
Dibanisa okanye thabatha ingcambu ka 81.

0:07:26.460,0:07:30.660
Sino thabatha 4 umphinda-phinda ngo thabatha 10.

0:07:30.660,0:07:31.870
Lento ngu thabatha 10.

0:07:31.870,0:07:33.280
Ndiyayazi ithesa kakhulu, ndiyaxolisa kakhulu

0:07:33.280,0:07:34.380
ngalonto, phinda-phinda ngo 1.

0:07:34.380,0:07:39.410
ngoko ke thabatha 4 uphinda-phinde ngo thabatha 10 ngu 40, onesichazi esingu dibanisa 40.

0:07:39.410,0:07:41.040
Dibanisa 40.

0:07:41.040,0:07:46.070
Kwaye kwangoko sinazo zonke phezu ko thabatha 20.

0:07:46.070,0:07:48.300
Kulungile, 81 dibanisa 40 ngu 121.

0:07:48.300,0:07:52.330
Ngoko ke lento ngu 9 dibanisa okanye thabatha ingcambu

0:07:52.330,0:07:58.290
ka 121 phezu ko thabatha 20.

0:07:58.290,0:08:01.620
Ingcambu ka 121 ngu 11.

0:08:01.620,0:08:03.170
Ngoko ke ndizohamba apha.

0:08:03.170,0:08:06.184
Ngethemba awuzose uyiphose indlela yalento ndiyenzayo.

0:08:06.184,0:08:13.720
Ngoko ke lento ngu 9 dibanisa oakanye thabatha 11, ngaphezu ko thabatha 20.

0:08:13.720,0:08:19.090
kwaye ngoko ke ukuba sithi 9 dibanisa 11 phezu ko thabatha 20, ngu 9

0:08:19.090,0:08:22.540
dibanisa 11 ngu 20, ngoko ke lenti ngu 20 phezu ko thabatha 20.

0:08:22.540,0:08:23.730
Ngoku cacileyo ulingana no thabatha 1.

0:08:23.730,0:08:24.900
Ngoko ke yigcambu enye.

0:08:24.900,0:08:28.260
Ngu 9 dibanisa--ngoba lento ngu dibanisa oaknye thabatha.

0:08:28.260,0:08:33.790
Kwaye enye ingcambu izakuba ngu 9 thabatha 11 phezu ko thabatha 20.

0:08:33.790,0:08:37.720
Ngokucacileyo ilingana no thabatha 2 phezu ko thabatha 20.

0:08:37.720,0:08:40.700
ngokucacileyo ilingana no 1 phezu ko 10.

0:08:40.700,0:08:42.690
ngoko ke ngenye ingcambu.

0:08:42.690,0:08:48.950
Ngoko ke ukuba bekunokufuneka ziyizobe phantsi lenxaki, besizokubona ukuba

0:08:48.950,0:08:52.640
ngokucacileyo idibana kumgca osembindini ka'x',

0:08:52.640,0:08:57.770
Okanye 'f' ka 'x' ulingana no0 kwincam ka'x' elingana no thabatha

0:08:57.770,0:09:01.690
1 kwaye 'x' ulingana no 1/10.

0:09:01.690,0:09:04.080
Ndizakwenza imizekelo eminizni kwicandelo lesibini, ngoba ndi

0:09:04.080,0:09:06.100
yacinga, ukuba nantoni na, ndingani bhidekisa

0:09:06.100,0:09:08.120
ngalena yodwa.

0:09:08.120,0:09:11.680
ngoko ke, ndizakunibona kwicandelo lesibini sisebenzisa

0:09:11.680,0:09:12.150
"quadratic equation".