4x^2+12x-5 eching

$$4 x ^ { 2 } + 12 x - 5$$

Omil

$$4\left(x-\frac{-\sqrt{14}-3}{2}\right)\left(x-\frac{\sqrt{14}-3}{2}\right)$$

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.

$$4x^{2}+12x-5=0$$

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.

$$x=\frac{-12±\sqrt{12^{2}-4\times 4\left(-5\right)}}{2\times 4}$$

12 kvadratini chiqarish.

$$x=\frac{-12±\sqrt{144-4\times 4\left(-5\right)}}{2\times 4}$$

-4 ni 4 marotabaga ko'paytirish.

$$x=\frac{-12±\sqrt{144-16\left(-5\right)}}{2\times 4}$$

-16 ni -5 marotabaga ko'paytirish.

$$x=\frac{-12±\sqrt{144+80}}{2\times 4}$$

144 ni 80 ga qo'shish.

$$x=\frac{-12±\sqrt{224}}{2\times 4}$$

224 ning kvadrat ildizini chiqarish.

$$x=\frac{-12±4\sqrt{14}}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{-12±4\sqrt{14}}{8}$$

x=\frac{-12±4\sqrt{14}}{8} tenglamasini yeching, bunda ± musbat. -12 ni 4\sqrt{14} ga qo'shish.

$$x=\frac{4\sqrt{14}-12}{8}$$

-12+4\sqrt{14} ni 8 ga bo'lish.

$$x=\frac{\sqrt{14}-3}{2}$$

x=\frac{-12±4\sqrt{14}}{8} tenglamasini yeching, bunda ± manfiy. -12 dan 4\sqrt{14} ni ayirish.

$$x=\frac{-4\sqrt{14}-12}{8}$$

-12-4\sqrt{14} ni 8 ga bo'lish.

$$x=\frac{-\sqrt{14}-3}{2}$$

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{14}}{2} ga va x_{2} uchun \frac{-3-\sqrt{14}}{2} ga bo‘ling.

$$4x^{2}+12x-5=4\left(x-\frac{\sqrt{14}-3}{2}\right)\left(x-\frac{-\sqrt{14}-3}{2}\right)$$

Baholash

$$4x^{2}+12x-5$$