Réitigh 11(1)=-10t^2+44t+30

$$11 ( 1 ) = - 10 t ^ { 2 } + 44 t + 30$$

Réitigh do t.

$$t=\frac{\sqrt{674}}{10}+\frac{11}{5}\approx 4.796150997$$

$$t=-\frac{\sqrt{674}}{10}+\frac{11}{5}\approx -0.396150997$$

Céimeanna ag Baint Úsáid as an bhFoirmle Chearnach

Méadaigh 11 agus 1 chun 11 a fháil.

$$11=-10t^{2}+44t+30$$

Athraigh na taobhanna ionas go mbeidh na téarmaí inathraitheacha ar fad ar an taobh clé.

$$-10t^{2}+44t+30=11$$

Bain 11 ón dá thaobh.

$$-10t^{2}+44t+30-11=0$$

Dealaigh 11 ó 30 chun 19 a fháil.

$$-10t^{2}+44t+19=0$$

Tá an chothromóid seo i bhfoirm chaighdeánach: ax^{2}+bx+c=0. Cuir -10 in ionad a, 44 in ionad b, agus 19 in ionad c san fhoirmle chearnach, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{-44±\sqrt{44^{2}-4\left(-10\right)\times 19}}{2\left(-10\right)}$$

Cearnóg 44.

$$t=\frac{-44±\sqrt{1936-4\left(-10\right)\times 19}}{2\left(-10\right)}$$

Méadaigh -4 faoi -10.

$$t=\frac{-44±\sqrt{1936+40\times 19}}{2\left(-10\right)}$$

Méadaigh 40 faoi 19.

$$t=\frac{-44±\sqrt{1936+760}}{2\left(-10\right)}$$

Suimigh 1936 le 760?

$$t=\frac{-44±\sqrt{2696}}{2\left(-10\right)}$$

Tóg fréamh chearnach 2696.

$$t=\frac{-44±2\sqrt{674}}{2\left(-10\right)}$$

Méadaigh 2 faoi -10.

$$t=\frac{-44±2\sqrt{674}}{-20}$$

Réitigh an chothromóid t=\frac{-44±2\sqrt{674}}{-20} nuair is ionann ± agus plus. Suimigh -44 le 2\sqrt{674}?

$$t=\frac{2\sqrt{674}-44}{-20}$$

Roinn -44+2\sqrt{674} faoi -20.

$$t=-\frac{\sqrt{674}}{10}+\frac{11}{5}$$

Réitigh an chothromóid t=\frac{-44±2\sqrt{674}}{-20} nuair is ionann ± agus míneas. Dealaigh 2\sqrt{674} ó -44.

$$t=\frac{-2\sqrt{674}-44}{-20}$$

Roinn -44-2\sqrt{674} faoi -20.

$$t=\frac{\sqrt{674}}{10}+\frac{11}{5}$$

Tá an chothromóid réitithe anois.

$$t=-\frac{\sqrt{674}}{10}+\frac{11}{5} t=\frac{\sqrt{674}}{10}+\frac{11}{5}$$

Céimeanna chun an Chearnóg a Chomhlánú

Méadaigh 11 agus 1 chun 11 a fháil.

$$11=-10t^{2}+44t+30$$

Athraigh na taobhanna ionas go mbeidh na téarmaí inathraitheacha ar fad ar an taobh clé.

$$-10t^{2}+44t+30=11$$

Bain 30 ón dá thaobh.

$$-10t^{2}+44t=11-30$$

Dealaigh 30 ó 11 chun -19 a fháil.

$$-10t^{2}+44t=-19$$

Roinn an dá thaobh faoi -10.

$$\frac{-10t^{2}+44t}{-10}=-\frac{19}{-10}$$

Má roinntear é faoi -10 cuirtear an iolrúchán faoi -10 ar ceal.

$$t^{2}+\frac{44}{-10}t=-\frac{19}{-10}$$

Laghdaigh an codán \frac{44}{-10} chuig na téarmaí is ísle trí 2 a bhaint agus a chealú.

$$t^{2}-\frac{22}{5}t=-\frac{19}{-10}$$

Roinn -19 faoi -10.

$$t^{2}-\frac{22}{5}t=\frac{19}{10}$$

Roinn -\frac{22}{5}, comhéifeacht an téarma x, faoi 2 chun -\frac{11}{5} a fháil. Ansin suimigh uimhir chearnach -\frac{11}{5} leis an dá thaobh den chothromóid. Déanann an chéim seo slánchearnóg de thaobh clé na cothromóide.

$$t^{2}-\frac{22}{5}t+\left(-\frac{11}{5}\right)^{2}=\frac{19}{10}+\left(-\frac{11}{5}\right)^{2}$$

Cearnaigh -\frac{11}{5} trí uimhreoir agus ainmneoir an chodáin a chearnú.

$$t^{2}-\frac{22}{5}t+\frac{121}{25}=\frac{19}{10}+\frac{121}{25}$$

Suimigh \frac{19}{10} le \frac{121}{25} trí chomhainmneoir a fháil agus na huimhreoirí a shuimiú. Laghdaigh an codán ansin go dtí na téarmaí is ísle más féidir.

$$t^{2}-\frac{22}{5}t+\frac{121}{25}=\frac{337}{50}$$

Fachtóirigh t^{2}-\frac{22}{5}t+\frac{121}{25}. Go ginearálta, nuair x^{2}+bx+c cearnóg fhoirfe é, is féidir é a fhachtóiriú i gcónaí mar \left(x+\frac{b}{2}\right)^{2}.

$$\left(t-\frac{11}{5}\right)^{2}=\frac{337}{50}$$

Tóg fréamh chearnach an dá thaobh den chothromóid.

$$\sqrt{\left(t-\frac{11}{5}\right)^{2}}=\sqrt{\frac{337}{50}}$$

Simpligh.

$$t-\frac{11}{5}=\frac{\sqrt{674}}{10} t-\frac{11}{5}=-\frac{\sqrt{674}}{10}$$

Cuir \frac{11}{5} leis an dá thaobh den chothromóid.

$$t=\frac{\sqrt{674}}{10}+\frac{11}{5} t=-\frac{\sqrt{674}}{10}+\frac{11}{5}$$