7x^2+6x-31 eching

$$7 x ^ { 2 } + 6 x - 31$$

Omil

$$7\left(x-\frac{-\sqrt{226}-3}{7}\right)\left(x-\frac{\sqrt{226}-3}{7}\right)$$

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.

$$7x^{2}+6x-31=0$$

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.

$$x=\frac{-6±\sqrt{6^{2}-4\times 7\left(-31\right)}}{2\times 7}$$

6 kvadratini chiqarish.

$$x=\frac{-6±\sqrt{36-4\times 7\left(-31\right)}}{2\times 7}$$

-4 ni 7 marotabaga ko'paytirish.

$$x=\frac{-6±\sqrt{36-28\left(-31\right)}}{2\times 7}$$

-28 ni -31 marotabaga ko'paytirish.

$$x=\frac{-6±\sqrt{36+868}}{2\times 7}$$

36 ni 868 ga qo'shish.

$$x=\frac{-6±\sqrt{904}}{2\times 7}$$

904 ning kvadrat ildizini chiqarish.

$$x=\frac{-6±2\sqrt{226}}{2\times 7}$$

2 ni 7 marotabaga ko'paytirish.

$$x=\frac{-6±2\sqrt{226}}{14}$$

x=\frac{-6±2\sqrt{226}}{14} tenglamasini yeching, bunda ± musbat. -6 ni 2\sqrt{226} ga qo'shish.

$$x=\frac{2\sqrt{226}-6}{14}$$

-6+2\sqrt{226} ni 14 ga bo'lish.

$$x=\frac{\sqrt{226}-3}{7}$$

x=\frac{-6±2\sqrt{226}}{14} tenglamasini yeching, bunda ± manfiy. -6 dan 2\sqrt{226} ni ayirish.

$$x=\frac{-2\sqrt{226}-6}{14}$$

-6-2\sqrt{226} ni 14 ga bo'lish.

$$x=\frac{-\sqrt{226}-3}{7}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{-3+\sqrt{226}}{7} ga va x_{2} uchun \frac{-3-\sqrt{226}}{7} ga bo‘ling.

$$7x^{2}+6x-31=7\left(x-\frac{\sqrt{226}-3}{7}\right)\left(x-\frac{-\sqrt{226}-3}{7}\right)$$

Baholash

$$7x^{2}+6x-31$$