2+8x-5x^2 eching

$$2 + 8 x - 5 x ^ { 2 }$$

Omil

$$-5\left(x-\frac{4-\sqrt{26}}{5}\right)\left(x-\frac{\sqrt{26}+4}{5}\right)$$

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.

$$-5x^{2}+8x+2=0$$

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.

$$x=\frac{-8±\sqrt{8^{2}-4\left(-5\right)\times 2}}{2\left(-5\right)}$$

8 kvadratini chiqarish.

$$x=\frac{-8±\sqrt{64-4\left(-5\right)\times 2}}{2\left(-5\right)}$$

-4 ni -5 marotabaga ko'paytirish.

$$x=\frac{-8±\sqrt{64+20\times 2}}{2\left(-5\right)}$$

20 ni 2 marotabaga ko'paytirish.

$$x=\frac{-8±\sqrt{64+40}}{2\left(-5\right)}$$

64 ni 40 ga qo'shish.

$$x=\frac{-8±\sqrt{104}}{2\left(-5\right)}$$

104 ning kvadrat ildizini chiqarish.

$$x=\frac{-8±2\sqrt{26}}{2\left(-5\right)}$$

2 ni -5 marotabaga ko'paytirish.

$$x=\frac{-8±2\sqrt{26}}{-10}$$

x=\frac{-8±2\sqrt{26}}{-10} tenglamasini yeching, bunda ± musbat. -8 ni 2\sqrt{26} ga qo'shish.

$$x=\frac{2\sqrt{26}-8}{-10}$$

-8+2\sqrt{26} ni -10 ga bo'lish.

$$x=\frac{4-\sqrt{26}}{5}$$

x=\frac{-8±2\sqrt{26}}{-10} tenglamasini yeching, bunda ± manfiy. -8 dan 2\sqrt{26} ni ayirish.

$$x=\frac{-2\sqrt{26}-8}{-10}$$

-8-2\sqrt{26} ni -10 ga bo'lish.

$$x=\frac{\sqrt{26}+4}{5}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{4-\sqrt{26}}{5} ga va x_{2} uchun \frac{4+\sqrt{26}}{5} ga bo‘ling.

$$-5x^{2}+8x+2=-5\left(x-\frac{4-\sqrt{26}}{5}\right)\left(x-\frac{\sqrt{26}+4}{5}\right)$$

Baholash

$$2+8x-5x^{2}$$