6x^2-2x-6 eching

$$6 x ^ { 2 } - 2 x - 6$$

Omil

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

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.

$$6x^{2}-2x-6=0$$

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.

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

-2 kvadratini chiqarish.

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

-4 ni 6 marotabaga ko'paytirish.

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

-24 ni -6 marotabaga ko'paytirish.

$$x=\frac{-\left(-2\right)±\sqrt{4+144}}{2\times 6}$$

4 ni 144 ga qo'shish.

$$x=\frac{-\left(-2\right)±\sqrt{148}}{2\times 6}$$

148 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-2\right)±2\sqrt{37}}{2\times 6}$$

-2 ning teskarisi 2 ga teng.

$$x=\frac{2±2\sqrt{37}}{2\times 6}$$

2 ni 6 marotabaga ko'paytirish.

$$x=\frac{2±2\sqrt{37}}{12}$$

x=\frac{2±2\sqrt{37}}{12} tenglamasini yeching, bunda ± musbat. 2 ni 2\sqrt{37} ga qo'shish.

$$x=\frac{2\sqrt{37}+2}{12}$$

2+2\sqrt{37} ni 12 ga bo'lish.

$$x=\frac{\sqrt{37}+1}{6}$$

x=\frac{2±2\sqrt{37}}{12} tenglamasini yeching, bunda ± manfiy. 2 dan 2\sqrt{37} ni ayirish.

$$x=\frac{2-2\sqrt{37}}{12}$$

2-2\sqrt{37} ni 12 ga bo'lish.

$$x=\frac{1-\sqrt{37}}{6}$$

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}}{6} ga va x_{2} uchun \frac{1-\sqrt{37}}{6} ga bo‘ling.

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

Baholash

$$6x^{2}-2x-6$$