Wmakelekile kumboniso yogqibezelo lesi kwere.
Yinto igqebezelo lwesi kwere?
Kulungile, yindlela yokusombulula i'quadratic equation".
Kwaye gqo, mandibhale phantsi i"quadratic equation', kwaye
kangoko ndzakubonisa kugqityezelwa njani isikwere.
Kwaye kangaoko sizakwenza omnye umzekelo, kwaye kwangako mhlawumbi singathetha
kancinci kutheni ibizwa ngokuba lugqibezelo lwesi kwere.
Ngoko ke masithi sinale nxaki: 'x' ophindwe kabini dibanisa '16x'
thabatha 57 ilingana no 0.
Ngoko ke zintoni izixhobo zethu kwizixhobo zethu apha
esinokuzisebenzisa ukusombulula lento?
Kulungile, singazama ukuyihlenga-hlengisa lento phandle.
Singathi, ngawaphi amanani othi uwadibanisa akunike u16, kwaye kangoko xa u-
uwaphinda-phinda akunike uthabatha 57?
Kwaye kuzakufuneka ucinge nayo kancinci.
Kwaye ungafumana onke amanani, kodwa awuka
qiniseki ukuba akhona amanani amabini apheleleyo angasebenza
nje kanjalo.
Kulenxaki akhona.
Kodwa uyazi kanjani, ngamanye amaxesha impendulo linani lesishumi
kwaye awuyazi lonto.
Ngoko ke, ngaxashanye ongahlenga-hlengisa kuxa uqinisekile ukuba
ungahlenga-hlengisa ngokwe ndlela yamanani apheleleyo.
Uyayazi, 'x' dibanisa inani elipheleleyo okanye 'x' thabatha elinye nje inani elipheleleyo
phinda-phinda, uyayazi, 'x' dibanisa namanye nje amanani apheleleyo.
Okanye njengesi qhelo.
Enye indlela kukwenza i"quadratic equation".
Kwaye into esiyenzayo ukubona yi"quadratic equation"
yindlela lanje imfutshane yokugqibezela isikwere.
I"quadratic equation" iyakwazeka ukuhlolwa ngokosebenzisa
ukugqibezela isikwere.
Ngoko ke yinto ukugqibezela isikwere?
Ngoko ke senza ntoni/
Kulungile, phambi kokuba siqubele kulomboniso masibone kwenzeka ntoni
xa ndiphinda-phinda inxaki ethile.
Mandiyenze phantsi apha.
Ngubani u'x' dibanisa 'a', uba phinda-phinde kabini.
Kulungile ilingana no 'x' ophindwe kabini dibanisa '2ax' dibanisa 'a' ophindwe kabini.
Kulungile.
Ngoko ke ukuba uabona nantoni na engalendlela, kufanele wazi
'x' dibanisa lonto ephindwe kabini.
Ngoko ke ibingazo bandle ukuba khange sinyanzele lenxaki
ngoko ke singayibhala ngalendlela 'x' dibanisa 'a' ophindwe kabini lingana nantoni,
kwaye kwangoko singathatha ingcambu?
Kwaye into esizakuyenza yile, gqo, yenza nje lonto.
Kwaye kukugqibezela isikwere.
Ngoko ke, mandikunike umzekelo.
Ndicinga umzekelo angayenza ibonakale ncono.
Mandibiyele lento phaya.
Lento yile kufuneka uyikhumbule.
Lento yonke ngumgaqo siseko oxhasa ukugqibezela isikwere--
ukufumana inxaki ibe ngoluhlobo, kwicala elinye
lenxaki, kwaye ube nenani kwelinye icala, ngoko ke
ungathatha ingcambu macala.
ngoko ke masibone.
Ekuqaleni, masiqale sijonge ukuba lento ayi
sosi kwere esigqibeleleyo.
Ukuba bekunjalo, umlinane bezakulingana no '2a'
kunjalo/
Ngoko ke 'a' bezakuba ngu 8, kwaye kwangoko lento ibizakuba ngu 64.
Lento icacile ayingo 64, ngoko ke lento ilapha ayi
phindwanga ngokuchazwa.
Ngoko ke, singenza ntoni/
Kulungile mandahlukane no 57 ndimahlule ngo 57 macala
ale nxaki.
Ngoko ke ndizakufumana 'x' ophindwe kabini dibanisa '16x' lingana no 57.
Yonke into endiyenzileyo ndidibanise 57 macala omabini alenxaki.
Ngoku yintoni itno endinokuyidibanisa ukuze lento, icala lasekhohlo
lalenxaki, lingaba liyaphindeka kabini
nje ngo 'x' dibanisa 'a'?
Ukuba uyalandela lomfuziselo pahntsi apha, sino 'x' ophindwe kabini
dibanisa '2ax'--ngoko ke ungayibona lento apha inje ngo '2ax'.
Akunjalo?
Ngu '2ax'.
Kwaye kwangoko kufuneka sidibanise 'a' ophindwe kabini kuyo.
Kunjalo/
Dibanisa 'a' ophindwe kabini.
Kwaye kwangoko sizakuba nendlela apha.
Kodwa siyayazi ukusukela kwamaqalela e"Algebra" ukuba nantoni na oyenzayo
kwlinye icala lenxaki kufuneka uyenze nakwelinye.
Ngoko ke sidibanise u'a' ophindwe kabini apha, ngoko ke masidibanise u 'a'
ophindwe kabini apha kwakhona.
Kwaye ngoku ungaphinda kwakhona uyibhale lento njenge sikwere
senye inxaki ethile.
Kodwa phambi kwalonto kufuneka sifumane ukuba ibiyintoni?
Kulungile, siyenza njani lanto?
Kulungile, ngubani u'a'?
Ukuba lenxaki ilapha ngu '2ax', ngubani u'a'?
Kulungile '2a' uzakulingana no 16, ngoko ke 'a' ulingana no8.
Kwaye ungayenza lanto ngokuhlolisisa;
yenza apha kuwe entloko.
Kodwa ukuba ubufuna yenzeke "algebraically" unga
bhala '2ax' ulingna
Kwaye kwangoko yahlula macala ngo '2x', kwaye ufumana u'a' eli
ngana no '16x' ngaphezu kuka '2x'
Kwaye uthathe ngathi 'x' akalingani no 0lento ehluza
Ngoko ke 'a' ngu 8.
Ngoko ke ukuba 'a' ngu 8singabhala lento kwakhona lenxaki--ndiza kucima
imibala ngoku pheleleyo-- nje ngokuba 'x' ophindwe kabini dibanisa '16x'
dibanisa 'a' ophindwe kabini.
Kulungile, ngu 64, ngoba 'a' ngu 8.
Ulingana no 57 dibanisa 64.
Akunjalo?
Ndiye kolona caciso ludinisayo apha, kodwa yonke
into esiyenzileyo ukufika phaya sidibanise 57 kumacala
omabini alenxaki ngendlela zokuyibeka kwicala lase kunene
kwaye kwangoko sidibanise 64 macala omabini alenxaki.
Kwaye kutheni sidibanisa 64 macala omabini alenxaki/
Ukuze ilicala lasekhohlo lalenxaki lithathe lendlela.
Kuba ngoku icala lasekhohlo lithathe lendlela
Ndingayibhla kwakhona kanjani?
'x' dibanisa 'a' , ubaphinde kabini.
Ndingayibhala kwakhona ngale ndlela.
kwaye siyayazi ukuba 'a' ngu 8, ngoko ke ivela ibe ngu 'x' dibanisa 8' ubaphinde kabini,
ilingana no--kwaye ngubani 57 dibanisa 64?
Ngu 121.
Ngoku sinento ekhangeleka ilula kakhulu--ngu
iseyi "quadratic equation", ngqo, ngoba ukuba u-
bunolwandisa elicala ubuzakufumana i'quadratic equation".
Kodwa singayisombulula lento ngaphndle kokusebenzisa i'quadratic equation".
okanye ngaphendle kokucazulula.
Usuka apho singathatha ingcambu yamacala omabini alento.`
Kwaye ukuba singathatha ingcambu yalama cala omabini singafumana ntoni?
Sifumana--kwakhona, ngokuqgibeleleyo masicime imibala--
la 'x' dibanisa 8 ulingana no, kwaye khumbula lento, udibanisa okanye
thabatha ingcambu ka 121.
Kwaye ngubani ingcambu ka 121?
Kulungile ngu 11, akunjalo/
Ngoko ke kwangoko singaza aph/
Mandibiyele lento phaya.
Lento ibubucala.
Ngoko ke sifumana 'x' dibanisa 8 ulingana no dibanisa okanye thabatha 11.
Kwaye ngoko ke 'x' ulingana no--thabatha 8 kumacala omabini--thabatha
8 dibanisa okanye thabatha 11.
Kwaye mgoko ke 'x' angalinga--ngoko ke thabatha 8 dibanisa 11 ngu 3.
Kunjalo?
Mandiqinisekise ndiyenzile lonto.
'x' ulingana no thabatha 8 dibaisa okanye thabatha 11.
Ewe.
Injalo.
Ngoko ke 'x' angaba ngu 3.
Kwaye kwangoko ukuba ndithatha uthabatha 8 thabatha 11, 'x' anga
lingana kwakhona no thabatha 19.
Kulungile.
Kwaye makhe sijonge ukuba lanto iyayenza imvakalelo.
Ngoko ke ngokwe ncazo eyingcingane lento ifanele ukucazululeka ngoku ka 'x'
thabatha 3 phinda-phinda 'x' dibanisa 19 ilingana no 0.
Kunjalo?
Ngoba zombini ezi zizisombululo zale nxaki.
Kwaye lonto iyasebenza, akunjalo?
Thabatha 3 uphinda-phinde ngo 19 gnu thabatha 57.
Kwaye thabatha 3 dibanisa 19 ngu dibanisa '16x'
Bekufanele kwangoko sicazulele lento kwaphaya, kodwa ukuba
lonto ibingacacanga kuthi--ngoba, uyayazi ubuncinci
19 ngamanye amaxesha linani elingaqhelekanga--besizakuyenza
sigqibezele isikwere.
Kwaye kutheni ibizwa ngokuba kukugqibezela isikwere?
Ngoba uyifumana ngalendlela kwaye kwangoko kufuneka udibanise lento
nantsi indlela yokugqibezela isikwere--ukuguqula lento
kwelicala lasekhohlo kwicala eliphindwe kabini.
Masenze enye yokugqibela.
Kwaye ndizakwenza ucaciso ulumbalwa kwaye kakhulu ukukhawulezisa
ukwenza inxaki, kwaye kwangoko ingenza ibonakale ilulu.
Kodwa lento izakuba yinxaki ekrwelisa isntloko.
Ngoko ke mandithi ndino '6x' ophindwe kabini thabatha '7x' thabatha 3 ngu 0.
Ungazama ukuyicazulula, kodwa ngokwenyani
ndiyathanda ukuyicazulula xa inomlingani.
Kwaye ungathi, kulungile kutheni singahluli ezizinto zombini macala
ezalenxaki ngo6?
Kodwa kwangoko ungazakufumana amaqhezu apha kunye neqhuzu nalapha.
Kwaye kuzimakakhulu ukuyicazulula nje ngokuyihlola.
Ungenza i"quadratic equation".
Kwaye mhlawumbi ndizakubonisa kwixesha elizayo lomboniso, i"quadratic
equation"--kwaye ndiyacinga ukuba ndiyenzile kwangaphambili apho ndinqginile
i"quadratic equation".
Kodwa i'quadratic equatio" ngamanye amagama
kukuqgibezela isikwere.
Ngundlela lula.
Kukukhumbula qha isichazi sayo.
Kodwa masigqibezele isikwere apha, ngoba yiyo into
esingayo apha kulomboniso.
Ngoko ke masidibanise u3 macala alenxaki.
Singenza--kakulhe, masidibanise u3 kuqala.
Ngoko ke ufumana u'6x' ophindwe kabini thabatha '7x' ilingana no3.
Ndidibanise u3 macala.
Kwaye abanye otitshala bazakumshiya uthabatha 3 apha, kwaye kwangoko zama
ukufumana phandle udibanisa ntoni kwaye yonke lonto.
Kodwa ndiyathanda ukuyibekela bucala kwendlela ukuze ndifiumana phandle
ngokucacileyo lileiphi inani endinokulibeka.
Kodwa kwakhona andimthandi lo 6 apha.
Uvele aziphixanise izinto.
Ndiathanda ukuba no'x' dibanisa 'a' ophindwe kabini, hayi ingcambu
umlingana wesimeli u'x'.
Ngoko ke masahlule macala ngo alanxaki ngo 6, kwaye ufumana
'x' ophindwe kabini thabatha 7/6x ulingana --3uamahlule ngo 6
ilingana no1/2.
Kwaye ngesiyenzile lanto inyathelo lethu lokuqala.
Ngesahlule ngo6 kwasekuqaleni kwinyathelo lethu lokuqala.
Ngenye indlela, masizame ukugqibezela isikwere.
Ngoko ke sino 'x' ophindwe kabini--ndikuvula indawo.
thabatha 7/6x dibanisa nalonto izakulingana no 1/2.
Kwaye ngoko ke, kufuneka sidibanise into apha ukuze elicala lasekhohlo
lenxaki iphume liyinto ephindwe kabini.
Ngoko ke siyenza njani lotno?
Kulungile ngocoselelo sijonga lomlingani, kwaye sibeke
engqondweni lento ayingo 7/6 ngu thabatha 7/6.
Uthatha 1/2 wayo, kwaye kwangoko umphinde kabini.
Kunjalo?
Mandiyenze.
'x' dibanisa 'a' , baphinde kabini ufumana u'x' ophindwe kabini dibanisa
'2ax' dibanisa 'a' ophindwe kabini.
Kunjalo?
Lento yeyonanto ekufuneka uyikhumbule maxesha onke.
Kuko konke ukugqibezela isikwere okukuqukayo.
Ngoko ke ndiqgibokuthini ngoku?
Kulungile, esisimeli sizakuba ngu 1/2 yalento
ingumlingani iphindwe kabnini.
Kwaye siyanzi njani lonto?
Ngoba 'a' uzakuba ngu 1/2 yalomlingani ukuba
wenza kancinci umfuziselo wokudibanisa.
Ngoko ke ngubani 1/2 walomlingani?
1/2 thabatha 7/6 ngu thabatha 7/12.
Ngoko ke ukuba ufuna ukubhala 'a' ulingana nothabatha
7/12 ngoko mzekelo.
Kwaye ndiphinda-phinde lento ngo 1/2.
Kunjalo?
Ngoko ke ndidibanisa ntoni macala omabini?
Ndidibanisa u'a' ophindwe kabini.
Ngoko ke ngubani u 7/12 umphinde kabini?
Kulungile ngubani u 49/144.`
Ukuba ndiyenzile kwicala lasekhohlo kufuneka ndiyenze
na kwcala lasekunene
Dibanisa 49/144.
Kwaye ngoku ndingacazulula njani elicala lasekhohlo?
Lithini inyathelo lehtu elilandelayo?
Kulungile siyazi ngoku yingcmbu egqibeleleyo.
Ngokwenyani, siyayazi ngubani u'a'. 'a' ngu thabatha 7/12.
Kwaye siyayazi icala lethu lasekhohlo lale nxaki
ngu 'x' thabatha 'a'--oaknye 'x' dibanisa 'a', kodwa 'a' linani lelithabatha yo.
Ngoko ke 'x' dibanisa 'a' kwaya 'a' nguthabatha, ohpindwe kabini.
Kwaye ukuba ufuna ungacazulula lento phandle kwaye ungqine
ukuba ukuba nyani ilingana nalento.
kwaye lanto izakulingana no--masifumane into ezifanayo
ngaphantsi, 144.
Ngoko ke 72 dibanisa 49 ilingana no121.
121/144.
Ngoko ke sino 'x' thabatha 7/12, yonke lanto uyiphnde ngesibini.
ilingana no 121/144.
Ngoko ke senza ntoni xa kunje ngoku?
Kulungile, ngoku sithatha ingcambu macala
aelnxaki.
Kwaye ndizama ukufumana indawo.
Tshintshela kuluhlaza.
Mandizibeke calanye ngaphandle.
kwaye sifumana 'x' thabatha 7/12 ulingana nodibanisa okanye thabatha
ingcambu yalanto.
Ngoko ke dibanisa okanye thabatha 11/12.
Kunjalo?
Ingcambuka 121 ngu 11.
Ingcambu ka 144 ngu 12.
Ngoko ke kwangoko singadibnisa 7/12 macala omabini elenxaki,
kwaye sifumana 'x' ulingana no 7/12 dibanisa okanye thabatha 11/12.
Kulungile lanto ilingana no 7 dibanisa oakanye thabatha 11/12.
Ngoko ke, athini amathuba ethu omabini?
7 dibanisa 11 ngu 18, ngaphesu kuka 12.
Ngoko ke 'x' angalingana 18/12, ngu 3/2.
okanye, ngubani 7 thabatha 11?
Ngu thabatha 4/12.
Ngoko ke ngu thabatha 1/3.
Nantsoke unayo.
Kuku gqibezela isikwere.
Ngethemba ufumene lanto inengcaciso enengeniso.
kwaye ukuba ufuna ukugqinelana ne"quadratic equation", konke owu
makukwenze endaweni yoba namanani apha, bhala 'ax' ophindwe kabini
dibanisa 'bx' dibanisa 'c' lingana no 0.
kwaye kwangoko gqibezela iskwere ngokusebenzisa a,b, kunye no c.
endaweni yamanani.
kwaye uzakuphela ne "quadratic equation'
ekupheleni.
Kwaye ndiyacinga ukuba ndiyenzile lanto kulomboniso.
Ndazise ukuba khange ndiyenze kwaye ndizakwenzea yona.
Ngenyindlela, ndizakubona kumboniso olandelayo.