Réitigh -32x^2/130^2+x=264

$$\frac { - 32 x ^ { 2 } } { 130 ^ { 2 } } + x = 264$$

Réitigh do x. (complex solution)

$$x=\frac{4225+65\sqrt{4223}i}{16}\approx 264.0625+263.999992602i$$

$$x=\frac{-65\sqrt{4223}i+4225}{16}\approx 264.0625-263.999992602i$$

Céimeanna ag Baint Úsáid as an bhFoirmle Chearnach

Ríomh cumhacht 130 de 2 agus faigh 16900.

$$\frac{-32x^{2}}{16900}+x=264$$

Roinn -32x^{2} faoi 16900 chun -\frac{8}{4225}x^{2} a fháil.

$$-\frac{8}{4225}x^{2}+x=264$$

Bain 264 ón dá thaobh.

$$-\frac{8}{4225}x^{2}+x-264=0$$

Tá an chothromóid seo i bhfoirm chaighdeánach: ax^{2}+bx+c=0. Cuir -\frac{8}{4225} in ionad a, 1 in ionad b, agus -264 in ionad c san fhoirmle chearnach, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-1±\sqrt{1^{2}-4\left(-\frac{8}{4225}\right)\left(-264\right)}}{2\left(-\frac{8}{4225}\right)}$$

Cearnóg 1.

$$x=\frac{-1±\sqrt{1-4\left(-\frac{8}{4225}\right)\left(-264\right)}}{2\left(-\frac{8}{4225}\right)}$$

Méadaigh -4 faoi -\frac{8}{4225}.

$$x=\frac{-1±\sqrt{1+\frac{32}{4225}\left(-264\right)}}{2\left(-\frac{8}{4225}\right)}$$

Méadaigh \frac{32}{4225} faoi -264.

$$x=\frac{-1±\sqrt{1-\frac{8448}{4225}}}{2\left(-\frac{8}{4225}\right)}$$

Suimigh 1 le -\frac{8448}{4225}?

$$x=\frac{-1±\sqrt{-\frac{4223}{4225}}}{2\left(-\frac{8}{4225}\right)}$$

Tóg fréamh chearnach -\frac{4223}{4225}.

$$x=\frac{-1±\frac{\sqrt{4223}i}{65}}{2\left(-\frac{8}{4225}\right)}$$

Méadaigh 2 faoi -\frac{8}{4225}.

$$x=\frac{-1±\frac{\sqrt{4223}i}{65}}{-\frac{16}{4225}}$$

Réitigh an chothromóid x=\frac{-1±\frac{\sqrt{4223}i}{65}}{-\frac{16}{4225}} nuair is ionann ± agus plus. Suimigh -1 le \frac{i\sqrt{4223}}{65}?

$$x=\frac{\frac{\sqrt{4223}i}{65}-1}{-\frac{16}{4225}}$$

Roinn -1+\frac{i\sqrt{4223}}{65} faoi -\frac{16}{4225} trí -1+\frac{i\sqrt{4223}}{65} a mhéadú faoi dheilín -\frac{16}{4225}.

$$x=\frac{-65\sqrt{4223}i+4225}{16}$$

Réitigh an chothromóid x=\frac{-1±\frac{\sqrt{4223}i}{65}}{-\frac{16}{4225}} nuair is ionann ± agus míneas. Dealaigh \frac{i\sqrt{4223}}{65} ó -1.

$$x=\frac{-\frac{\sqrt{4223}i}{65}-1}{-\frac{16}{4225}}$$

Roinn -1-\frac{i\sqrt{4223}}{65} faoi -\frac{16}{4225} trí -1-\frac{i\sqrt{4223}}{65} a mhéadú faoi dheilín -\frac{16}{4225}.

$$x=\frac{4225+65\sqrt{4223}i}{16}$$

Tá an chothromóid réitithe anois.

$$x=\frac{-65\sqrt{4223}i+4225}{16} x=\frac{4225+65\sqrt{4223}i}{16}$$

Céimeanna chun an Chearnóg a Chomhlánú

Ríomh cumhacht 130 de 2 agus faigh 16900.

$$\frac{-32x^{2}}{16900}+x=264$$

Roinn -32x^{2} faoi 16900 chun -\frac{8}{4225}x^{2} a fháil.

$$-\frac{8}{4225}x^{2}+x=264$$

Roinn an dá thaobh den chothromóid faoi -\frac{8}{4225}, arb ionann é sin agus an dá thaobh a mhéadú faoi dheilín an chodáin.

$$\frac{-\frac{8}{4225}x^{2}+x}{-\frac{8}{4225}}=\frac{264}{-\frac{8}{4225}}$$

Má roinntear é faoi -\frac{8}{4225} cuirtear an iolrúchán faoi -\frac{8}{4225} ar ceal.

$$x^{2}+\frac{1}{-\frac{8}{4225}}x=\frac{264}{-\frac{8}{4225}}$$

Roinn 1 faoi -\frac{8}{4225} trí 1 a mhéadú faoi dheilín -\frac{8}{4225}.

$$x^{2}-\frac{4225}{8}x=\frac{264}{-\frac{8}{4225}}$$

Roinn 264 faoi -\frac{8}{4225} trí 264 a mhéadú faoi dheilín -\frac{8}{4225}.

$$x^{2}-\frac{4225}{8}x=-139425$$

Roinn -\frac{4225}{8}, comhéifeacht an téarma x, faoi 2 chun -\frac{4225}{16} a fháil. Ansin suimigh uimhir chearnach -\frac{4225}{16} leis an dá thaobh den chothromóid. Déanann an chéim seo slánchearnóg de thaobh clé na cothromóide.

$$x^{2}-\frac{4225}{8}x+\left(-\frac{4225}{16}\right)^{2}=-139425+\left(-\frac{4225}{16}\right)^{2}$$

Cearnaigh -\frac{4225}{16} trí uimhreoir agus ainmneoir an chodáin a chearnú.

$$x^{2}-\frac{4225}{8}x+\frac{17850625}{256}=-139425+\frac{17850625}{256}$$

Suimigh -139425 le \frac{17850625}{256}?

$$x^{2}-\frac{4225}{8}x+\frac{17850625}{256}=-\frac{17842175}{256}$$

Fachtóirigh x^{2}-\frac{4225}{8}x+\frac{17850625}{256}. 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}.

$$\left(x-\frac{4225}{16}\right)^{2}=-\frac{17842175}{256}$$

Tóg fréamh chearnach an dá thaobh den chothromóid.

$$\sqrt{\left(x-\frac{4225}{16}\right)^{2}}=\sqrt{-\frac{17842175}{256}}$$

Simpligh.

$$x-\frac{4225}{16}=\frac{65\sqrt{4223}i}{16} x-\frac{4225}{16}=-\frac{65\sqrt{4223}i}{16}$$

Cuir \frac{4225}{16} leis an dá thaobh den chothromóid.

$$x=\frac{4225+65\sqrt{4223}i}{16} x=\frac{-65\sqrt{4223}i+4225}{16}$$