9x^2+12x-2 eching

$$9 { x }^{ 2 } +12x-2$$

Omil

$$9\left(x-\frac{-\sqrt{6}-2}{3}\right)\left(x-\frac{\sqrt{6}-2}{3}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

Kvadrat koʻp tenglama bu orqali hisoblanadi: ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), bu yerda x_{1} va x_{2} ax^{2}+bx+c=0 kvadrat tenglamaning yechimlari.

$$9x^{2}+12x-2=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$x=\frac{-12±\sqrt{12^{2}-4\times 9\left(-2\right)}}{2\times 9}$$

12 kvadratini chiqarish.

$$x=\frac{-12±\sqrt{144-4\times 9\left(-2\right)}}{2\times 9}$$

-4 ni 9 marotabaga ko'paytirish.

$$x=\frac{-12±\sqrt{144-36\left(-2\right)}}{2\times 9}$$

-36 ni -2 marotabaga ko'paytirish.

$$x=\frac{-12±\sqrt{144+72}}{2\times 9}$$

144 ni 72 ga qo'shish.

$$x=\frac{-12±\sqrt{216}}{2\times 9}$$

216 ning kvadrat ildizini chiqarish.

$$x=\frac{-12±6\sqrt{6}}{2\times 9}$$

2 ni 9 marotabaga ko'paytirish.

$$x=\frac{-12±6\sqrt{6}}{18}$$

x=\frac{-12±6\sqrt{6}}{18} tenglamasini yeching, bunda ± musbat. -12 ni 6\sqrt{6} ga qo'shish.

$$x=\frac{6\sqrt{6}-12}{18}$$

-12+6\sqrt{6} ni 18 ga bo'lish.

$$x=\frac{\sqrt{6}-2}{3}$$

x=\frac{-12±6\sqrt{6}}{18} tenglamasini yeching, bunda ± manfiy. -12 dan 6\sqrt{6} ni ayirish.

$$x=\frac{-6\sqrt{6}-12}{18}$$

-12-6\sqrt{6} ni 18 ga bo'lish.

$$x=\frac{-\sqrt{6}-2}{3}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{-2+\sqrt{6}}{3} ga va x_{2} uchun \frac{-2-\sqrt{6}}{3} ga bo‘ling.

$$9x^{2}+12x-2=9\left(x-\frac{\sqrt{6}-2}{3}\right)\left(x-\frac{-\sqrt{6}-2}{3}\right)$$

Baholash

$$9x^{2}+12x-2$$