Réitigh 18000=-q^2-2q+534

$$18000 = - q ^ { 2 } - 2 q + 534$$

Réitigh do q.

$$q=-\sqrt{17465}i-1\approx -1-132.155211778i$$

$$q=-1+\sqrt{17465}i\approx -1+132.155211778i$$

Céimeanna ag Baint Úsáid as an bhFoirmle Chearnach

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

$$-q^{2}-2q+534=18000$$

Bain 18000 ón dá thaobh.

$$-q^{2}-2q+534-18000=0$$

Dealaigh 18000 ó 534 chun -17466 a fháil.

$$-q^{2}-2q-17466=0$$

Tá an chothromóid seo i bhfoirm chaighdeánach: ax^{2}+bx+c=0. Cuir -1 in ionad a, -2 in ionad b, agus -17466 in ionad c san fhoirmle chearnach, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$q=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-1\right)\left(-17466\right)}}{2\left(-1\right)}$$

Cearnóg -2.

$$q=\frac{-\left(-2\right)±\sqrt{4-4\left(-1\right)\left(-17466\right)}}{2\left(-1\right)}$$

Méadaigh -4 faoi -1.

$$q=\frac{-\left(-2\right)±\sqrt{4+4\left(-17466\right)}}{2\left(-1\right)}$$

Méadaigh 4 faoi -17466.

$$q=\frac{-\left(-2\right)±\sqrt{4-69864}}{2\left(-1\right)}$$

Suimigh 4 le -69864?

$$q=\frac{-\left(-2\right)±\sqrt{-69860}}{2\left(-1\right)}$$

Tóg fréamh chearnach -69860.

$$q=\frac{-\left(-2\right)±2\sqrt{17465}i}{2\left(-1\right)}$$

Tá 2 urchomhairleach le -2.

$$q=\frac{2±2\sqrt{17465}i}{2\left(-1\right)}$$

Méadaigh 2 faoi -1.

$$q=\frac{2±2\sqrt{17465}i}{-2}$$

Réitigh an chothromóid q=\frac{2±2\sqrt{17465}i}{-2} nuair is ionann ± agus plus. Suimigh 2 le 2i\sqrt{17465}?

$$q=\frac{2+2\sqrt{17465}i}{-2}$$

Roinn 2+2i\sqrt{17465} faoi -2.

$$q=-\sqrt{17465}i-1$$

Réitigh an chothromóid q=\frac{2±2\sqrt{17465}i}{-2} nuair is ionann ± agus míneas. Dealaigh 2i\sqrt{17465} ó 2.

$$q=\frac{-2\sqrt{17465}i+2}{-2}$$

Roinn 2-2i\sqrt{17465} faoi -2.

$$q=-1+\sqrt{17465}i$$

Tá an chothromóid réitithe anois.

$$q=-\sqrt{17465}i-1 q=-1+\sqrt{17465}i$$

Céimeanna chun an Chearnóg a Chomhlánú

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

$$-q^{2}-2q+534=18000$$

Bain 534 ón dá thaobh.

$$-q^{2}-2q=18000-534$$

Dealaigh 534 ó 18000 chun 17466 a fháil.

$$-q^{2}-2q=17466$$

Roinn an dá thaobh faoi -1.

$$\frac{-q^{2}-2q}{-1}=\frac{17466}{-1}$$

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

$$q^{2}+\left(-\frac{2}{-1}\right)q=\frac{17466}{-1}$$

Roinn -2 faoi -1.

$$q^{2}+2q=\frac{17466}{-1}$$

Roinn 17466 faoi -1.

$$q^{2}+2q=-17466$$

Roinn 2, comhéifeacht an téarma x, faoi 2 chun 1 a fháil. Ansin suimigh uimhir chearnach 1 leis an dá thaobh den chothromóid. Déanann an chéim seo slánchearnóg de thaobh clé na cothromóide.

$$q^{2}+2q+1^{2}=-17466+1^{2}$$

Cearnóg 1.

$$q^{2}+2q+1=-17466+1$$

Suimigh -17466 le 1?

$$q^{2}+2q+1=-17465$$

Fachtóirigh q^{2}+2q+1. 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}.

$$\left(q+1\right)^{2}=-17465$$

Tóg fréamh chearnach an dá thaobh den chothromóid.

$$\sqrt{\left(q+1\right)^{2}}=\sqrt{-17465}$$

Simpligh.

$$q+1=\sqrt{17465}i q+1=-\sqrt{17465}i$$

Bain 1 ón dá thaobh den chothromóid.

$$q=-1+\sqrt{17465}i q=-\sqrt{17465}i-1$$