5x^2-6x-2 eching

$$5 { x }^{ 2 } -6x-2$$

Omil

$$5\left(x-\frac{3-\sqrt{19}}{5}\right)\left(x-\frac{\sqrt{19}+3}{5}\right)$$

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.

$$5x^{2}-6x-2=0$$

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.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\times 5\left(-2\right)}}{2\times 5}$$

-6 kvadratini chiqarish.

$$x=\frac{-\left(-6\right)±\sqrt{36-4\times 5\left(-2\right)}}{2\times 5}$$

-4 ni 5 marotabaga ko'paytirish.

$$x=\frac{-\left(-6\right)±\sqrt{36-20\left(-2\right)}}{2\times 5}$$

-20 ni -2 marotabaga ko'paytirish.

$$x=\frac{-\left(-6\right)±\sqrt{36+40}}{2\times 5}$$

36 ni 40 ga qo'shish.

$$x=\frac{-\left(-6\right)±\sqrt{76}}{2\times 5}$$

76 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-6\right)±2\sqrt{19}}{2\times 5}$$

-6 ning teskarisi 6 ga teng.

$$x=\frac{6±2\sqrt{19}}{2\times 5}$$

2 ni 5 marotabaga ko'paytirish.

$$x=\frac{6±2\sqrt{19}}{10}$$

x=\frac{6±2\sqrt{19}}{10} tenglamasini yeching, bunda ± musbat. 6 ni 2\sqrt{19} ga qo'shish.

$$x=\frac{2\sqrt{19}+6}{10}$$

6+2\sqrt{19} ni 10 ga bo'lish.

$$x=\frac{\sqrt{19}+3}{5}$$

x=\frac{6±2\sqrt{19}}{10} tenglamasini yeching, bunda ± manfiy. 6 dan 2\sqrt{19} ni ayirish.

$$x=\frac{6-2\sqrt{19}}{10}$$

6-2\sqrt{19} ni 10 ga bo'lish.

$$x=\frac{3-\sqrt{19}}{5}$$

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{19}}{5} ga va x_{2} uchun \frac{3-\sqrt{19}}{5} ga bo‘ling.

$$5x^{2}-6x-2=5\left(x-\frac{\sqrt{19}+3}{5}\right)\left(x-\frac{3-\sqrt{19}}{5}\right)$$

Baholash

$$5x^{2}-6x-2$$