Réitigh 300q-2q^2-100-q^2

$$300 q - 2 q ^ { 2 } - 100 - q ^ { 2 }$$

Fachtóirigh

$$-3\left(q-\left(-\frac{10\sqrt{222}}{3}+50\right)\right)\left(q-\left(\frac{10\sqrt{222}}{3}+50\right)\right)$$

Céimeanna ag Baint Úsáid as an bhFoirmle Chearnach

Comhcheangail -2q^{2} agus -q^{2} chun -3q^{2} a fháil.

$$factor(300q-3q^{2}-100)$$

Is féidir an trasfhoirmiú ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) a úsáid chun luach iltéarmach cearnach a fhachtóiriú, nuair is réitigh iad x_{1} agus x_{2} ar an gcothromóid chearnach ax^{2}+bx+c=0.

$$-3q^{2}+300q-100=0$$

Is féidir gach cothromóid san fhoirm ax^{2}+bx+c=0 a réiteach ag baint úsáid as an bhfoirmle chearnach : \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Tugann an fhoirmle chearnach dhá réiteach, ceann amháin nuair is suimiú é ± agus ceann eile nuair is dealú é.

$$q=\frac{-300±\sqrt{300^{2}-4\left(-3\right)\left(-100\right)}}{2\left(-3\right)}$$

Cearnóg 300.

$$q=\frac{-300±\sqrt{90000-4\left(-3\right)\left(-100\right)}}{2\left(-3\right)}$$

Méadaigh -4 faoi -3.

$$q=\frac{-300±\sqrt{90000+12\left(-100\right)}}{2\left(-3\right)}$$

Méadaigh 12 faoi -100.

$$q=\frac{-300±\sqrt{90000-1200}}{2\left(-3\right)}$$

Suimigh 90000 le -1200?

$$q=\frac{-300±\sqrt{88800}}{2\left(-3\right)}$$

Tóg fréamh chearnach 88800.

$$q=\frac{-300±20\sqrt{222}}{2\left(-3\right)}$$

Méadaigh 2 faoi -3.

$$q=\frac{-300±20\sqrt{222}}{-6}$$

Réitigh an chothromóid q=\frac{-300±20\sqrt{222}}{-6} nuair is ionann ± agus plus. Suimigh -300 le 20\sqrt{222}?

$$q=\frac{20\sqrt{222}-300}{-6}$$

Roinn -300+20\sqrt{222} faoi -6.

$$q=-\frac{10\sqrt{222}}{3}+50$$

Réitigh an chothromóid q=\frac{-300±20\sqrt{222}}{-6} nuair is ionann ± agus míneas. Dealaigh 20\sqrt{222} ó -300.

$$q=\frac{-20\sqrt{222}-300}{-6}$$

Roinn -300-20\sqrt{222} faoi -6.

$$q=\frac{10\sqrt{222}}{3}+50$$

Úsáid ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) chun an slonn bunaidh a fhachtóiriú. Cuir 50-\frac{10\sqrt{222}}{3} in ionad x_{1} agus 50+\frac{10\sqrt{222}}{3} in ionad x_{2}.

$$-3q^{2}+300q-100=-3\left(q-\left(-\frac{10\sqrt{222}}{3}+50\right)\right)\left(q-\left(\frac{10\sqrt{222}}{3}+50\right)\right)$$

Luacháil

$$-3q^{2}+300q-100$$

Céimeanna Réitigh

Comhcheangail -2q^{2} agus -q^{2} chun -3q^{2} a fháil.

$$300q-3q^{2}-100$$