6x^2+4x-24 eching

$$6 { x }^{ 2 } +4x-24$$

Omil

$$6\left(x-\frac{-\sqrt{37}-1}{3}\right)\left(x-\frac{\sqrt{37}-1}{3}\right)$$

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.

$$6x^{2}+4x-24=0$$

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.

$$x=\frac{-4±\sqrt{4^{2}-4\times 6\left(-24\right)}}{2\times 6}$$

4 kvadratini chiqarish.

$$x=\frac{-4±\sqrt{16-4\times 6\left(-24\right)}}{2\times 6}$$

-4 ni 6 marotabaga ko'paytirish.

$$x=\frac{-4±\sqrt{16-24\left(-24\right)}}{2\times 6}$$

-24 ni -24 marotabaga ko'paytirish.

$$x=\frac{-4±\sqrt{16+576}}{2\times 6}$$

16 ni 576 ga qo'shish.

$$x=\frac{-4±\sqrt{592}}{2\times 6}$$

592 ning kvadrat ildizini chiqarish.

$$x=\frac{-4±4\sqrt{37}}{2\times 6}$$

2 ni 6 marotabaga ko'paytirish.

$$x=\frac{-4±4\sqrt{37}}{12}$$

x=\frac{-4±4\sqrt{37}}{12} tenglamasini yeching, bunda ± musbat. -4 ni 4\sqrt{37} ga qo'shish.

$$x=\frac{4\sqrt{37}-4}{12}$$

-4+4\sqrt{37} ni 12 ga bo'lish.

$$x=\frac{\sqrt{37}-1}{3}$$

x=\frac{-4±4\sqrt{37}}{12} tenglamasini yeching, bunda ± manfiy. -4 dan 4\sqrt{37} ni ayirish.

$$x=\frac{-4\sqrt{37}-4}{12}$$

-4-4\sqrt{37} ni 12 ga bo'lish.

$$x=\frac{-\sqrt{37}-1}{3}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{-1+\sqrt{37}}{3} ga va x_{2} uchun \frac{-1-\sqrt{37}}{3} ga bo‘ling.

$$6x^{2}+4x-24=6\left(x-\frac{\sqrt{37}-1}{3}\right)\left(x-\frac{-\sqrt{37}-1}{3}\right)$$

Baholash

$$6x^{2}+4x-24$$