4x^2+14x-12 eching

$$4 x ^ { 2 } + 14 x - 12$$

Omil

$$4\left(x-\frac{-\sqrt{97}-7}{4}\right)\left(x-\frac{\sqrt{97}-7}{4}\right)$$

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.

$$4x^{2}+14x-12=0$$

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.

$$x=\frac{-14±\sqrt{14^{2}-4\times 4\left(-12\right)}}{2\times 4}$$

14 kvadratini chiqarish.

$$x=\frac{-14±\sqrt{196-4\times 4\left(-12\right)}}{2\times 4}$$

-4 ni 4 marotabaga ko'paytirish.

$$x=\frac{-14±\sqrt{196-16\left(-12\right)}}{2\times 4}$$

-16 ni -12 marotabaga ko'paytirish.

$$x=\frac{-14±\sqrt{196+192}}{2\times 4}$$

196 ni 192 ga qo'shish.

$$x=\frac{-14±\sqrt{388}}{2\times 4}$$

388 ning kvadrat ildizini chiqarish.

$$x=\frac{-14±2\sqrt{97}}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{-14±2\sqrt{97}}{8}$$

x=\frac{-14±2\sqrt{97}}{8} tenglamasini yeching, bunda ± musbat. -14 ni 2\sqrt{97} ga qo'shish.

$$x=\frac{2\sqrt{97}-14}{8}$$

-14+2\sqrt{97} ni 8 ga bo'lish.

$$x=\frac{\sqrt{97}-7}{4}$$

x=\frac{-14±2\sqrt{97}}{8} tenglamasini yeching, bunda ± manfiy. -14 dan 2\sqrt{97} ni ayirish.

$$x=\frac{-2\sqrt{97}-14}{8}$$

-14-2\sqrt{97} ni 8 ga bo'lish.

$$x=\frac{-\sqrt{97}-7}{4}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{-7+\sqrt{97}}{4} ga va x_{2} uchun \frac{-7-\sqrt{97}}{4} ga bo‘ling.

$$4x^{2}+14x-12=4\left(x-\frac{\sqrt{97}-7}{4}\right)\left(x-\frac{-\sqrt{97}-7}{4}\right)$$

Baholash

$$4x^{2}+14x-12$$