5x^2+20x-2 eching

$$5 { x }^{ 2 } +20x-2$$

Omil

$$5\left(x-\left(-\frac{\sqrt{110}}{5}-2\right)\right)\left(x-\left(\frac{\sqrt{110}}{5}-2\right)\right)$$

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.

$$5x^{2}+20x-2=0$$

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.

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

20 kvadratini chiqarish.

$$x=\frac{-20±\sqrt{400-4\times 5\left(-2\right)}}{2\times 5}$$

-4 ni 5 marotabaga ko'paytirish.

$$x=\frac{-20±\sqrt{400-20\left(-2\right)}}{2\times 5}$$

-20 ni -2 marotabaga ko'paytirish.

$$x=\frac{-20±\sqrt{400+40}}{2\times 5}$$

400 ni 40 ga qo'shish.

$$x=\frac{-20±\sqrt{440}}{2\times 5}$$

440 ning kvadrat ildizini chiqarish.

$$x=\frac{-20±2\sqrt{110}}{2\times 5}$$

2 ni 5 marotabaga ko'paytirish.

$$x=\frac{-20±2\sqrt{110}}{10}$$

x=\frac{-20±2\sqrt{110}}{10} tenglamasini yeching, bunda ± musbat. -20 ni 2\sqrt{110} ga qo'shish.

$$x=\frac{2\sqrt{110}-20}{10}$$

-20+2\sqrt{110} ni 10 ga bo'lish.

$$x=\frac{\sqrt{110}}{5}-2$$

x=\frac{-20±2\sqrt{110}}{10} tenglamasini yeching, bunda ± manfiy. -20 dan 2\sqrt{110} ni ayirish.

$$x=\frac{-2\sqrt{110}-20}{10}$$

-20-2\sqrt{110} ni 10 ga bo'lish.

$$x=-\frac{\sqrt{110}}{5}-2$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun -2+\frac{\sqrt{110}}{5} ga va x_{2} uchun -2-\frac{\sqrt{110}}{5} ga bo‘ling.

$$5x^{2}+20x-2=5\left(x-\left(\frac{\sqrt{110}}{5}-2\right)\right)\left(x-\left(-\frac{\sqrt{110}}{5}-2\right)\right)$$

Baholash

$$5x^{2}+20x-2$$