Réitigh 4t^2-64t+256=5t^2+36

$$4 t ^ { 2 } - 64 t + 256 = 5 t ^ { 2 } + 36$$

Réitigh do t.

$$t=2\sqrt{311}-32\approx 3.270384177$$

$$t=-2\sqrt{311}-32\approx -67.270384177$$

Céimeanna ag Baint Úsáid as an bhFoirmle Chearnach

Bain 5t^{2} ón dá thaobh.

$$4t^{2}-64t+256-5t^{2}=36$$

Comhcheangail 4t^{2} agus -5t^{2} chun -t^{2} a fháil.

$$-t^{2}-64t+256=36$$

Bain 36 ón dá thaobh.

$$-t^{2}-64t+256-36=0$$

Dealaigh 36 ó 256 chun 220 a fháil.

$$-t^{2}-64t+220=0$$

Tá an chothromóid seo i bhfoirm chaighdeánach: ax^{2}+bx+c=0. Cuir -1 in ionad a, -64 in ionad b, agus 220 in ionad c san fhoirmle chearnach, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{-\left(-64\right)±\sqrt{\left(-64\right)^{2}-4\left(-1\right)\times 220}}{2\left(-1\right)}$$

Cearnóg -64.

$$t=\frac{-\left(-64\right)±\sqrt{4096-4\left(-1\right)\times 220}}{2\left(-1\right)}$$

Méadaigh -4 faoi -1.

$$t=\frac{-\left(-64\right)±\sqrt{4096+4\times 220}}{2\left(-1\right)}$$

Méadaigh 4 faoi 220.

$$t=\frac{-\left(-64\right)±\sqrt{4096+880}}{2\left(-1\right)}$$

Suimigh 4096 le 880?

$$t=\frac{-\left(-64\right)±\sqrt{4976}}{2\left(-1\right)}$$

Tóg fréamh chearnach 4976.

$$t=\frac{-\left(-64\right)±4\sqrt{311}}{2\left(-1\right)}$$

Tá 64 urchomhairleach le -64.

$$t=\frac{64±4\sqrt{311}}{2\left(-1\right)}$$

Méadaigh 2 faoi -1.

$$t=\frac{64±4\sqrt{311}}{-2}$$

Réitigh an chothromóid t=\frac{64±4\sqrt{311}}{-2} nuair is ionann ± agus plus. Suimigh 64 le 4\sqrt{311}?

$$t=\frac{4\sqrt{311}+64}{-2}$$

Roinn 64+4\sqrt{311} faoi -2.

$$t=-2\sqrt{311}-32$$

Réitigh an chothromóid t=\frac{64±4\sqrt{311}}{-2} nuair is ionann ± agus míneas. Dealaigh 4\sqrt{311} ó 64.

$$t=\frac{64-4\sqrt{311}}{-2}$$

Roinn 64-4\sqrt{311} faoi -2.

$$t=2\sqrt{311}-32$$

Tá an chothromóid réitithe anois.

$$t=-2\sqrt{311}-32 t=2\sqrt{311}-32$$

Céimeanna chun an Chearnóg a Chomhlánú

Bain 5t^{2} ón dá thaobh.

$$4t^{2}-64t+256-5t^{2}=36$$

Comhcheangail 4t^{2} agus -5t^{2} chun -t^{2} a fháil.

$$-t^{2}-64t+256=36$$

Bain 256 ón dá thaobh.

$$-t^{2}-64t=36-256$$

Dealaigh 256 ó 36 chun -220 a fháil.

$$-t^{2}-64t=-220$$

Roinn an dá thaobh faoi -1.

$$\frac{-t^{2}-64t}{-1}=-\frac{220}{-1}$$

Má roinntear é faoi -1 cuirtear an iolrúchán faoi -1 ar ceal.

$$t^{2}+\left(-\frac{64}{-1}\right)t=-\frac{220}{-1}$$

Roinn -64 faoi -1.

$$t^{2}+64t=-\frac{220}{-1}$$

Roinn -220 faoi -1.

$$t^{2}+64t=220$$

Roinn 64, comhéifeacht an téarma x, faoi 2 chun 32 a fháil. Ansin suimigh uimhir chearnach 32 leis an dá thaobh den chothromóid. Déanann an chéim seo slánchearnóg de thaobh clé na cothromóide.

$$t^{2}+64t+32^{2}=220+32^{2}$$

Cearnóg 32.

$$t^{2}+64t+1024=220+1024$$

Suimigh 220 le 1024?

$$t^{2}+64t+1024=1244$$

Fachtóirigh t^{2}+64t+1024. 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}.

$$\left(t+32\right)^{2}=1244$$

Tóg fréamh chearnach an dá thaobh den chothromóid.

$$\sqrt{\left(t+32\right)^{2}}=\sqrt{1244}$$

Simpligh.

$$t+32=2\sqrt{311} t+32=-2\sqrt{311}$$

Bain 32 ón dá thaobh den chothromóid.

$$t=2\sqrt{311}-32 t=-2\sqrt{311}-32$$