5x^2-2x-2 eching

$$5 x ^ { 2 } - 2 x - 2$$

Omil

$$5\left(x-\frac{1-\sqrt{11}}{5}\right)\left(x-\frac{\sqrt{11}+1}{5}\right)$$

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.

$$5x^{2}-2x-2=0$$

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.

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

-2 kvadratini chiqarish.

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

-4 ni 5 marotabaga ko'paytirish.

$$x=\frac{-\left(-2\right)±\sqrt{4-20\left(-2\right)}}{2\times 5}$$

-20 ni -2 marotabaga ko'paytirish.

$$x=\frac{-\left(-2\right)±\sqrt{4+40}}{2\times 5}$$

4 ni 40 ga qo'shish.

$$x=\frac{-\left(-2\right)±\sqrt{44}}{2\times 5}$$

44 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-2\right)±2\sqrt{11}}{2\times 5}$$

-2 ning teskarisi 2 ga teng.

$$x=\frac{2±2\sqrt{11}}{2\times 5}$$

2 ni 5 marotabaga ko'paytirish.

$$x=\frac{2±2\sqrt{11}}{10}$$

x=\frac{2±2\sqrt{11}}{10} tenglamasini yeching, bunda ± musbat. 2 ni 2\sqrt{11} ga qo'shish.

$$x=\frac{2\sqrt{11}+2}{10}$$

2+2\sqrt{11} ni 10 ga bo'lish.

$$x=\frac{\sqrt{11}+1}{5}$$

x=\frac{2±2\sqrt{11}}{10} tenglamasini yeching, bunda ± manfiy. 2 dan 2\sqrt{11} ni ayirish.

$$x=\frac{2-2\sqrt{11}}{10}$$

2-2\sqrt{11} ni 10 ga bo'lish.

$$x=\frac{1-\sqrt{11}}{5}$$

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{11}}{5} ga va x_{2} uchun \frac{1-\sqrt{11}}{5} ga bo‘ling.

$$5x^{2}-2x-2=5\left(x-\frac{\sqrt{11}+1}{5}\right)\left(x-\frac{1-\sqrt{11}}{5}\right)$$

Baholash

$$5x^{2}-2x-2$$