Isihloko: Ugqibezelo lesi kwere

Khan Academy's video on completing the square.

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.