5x^2+48x-91 eching

$$5 { x }^{ 2 } +48x-91$$

Omil

$$5\left(x-\frac{-\sqrt{1031}-24}{5}\right)\left(x-\frac{\sqrt{1031}-24}{5}\right)$$

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.

$$5x^{2}+48x-91=0$$

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.

$$x=\frac{-48±\sqrt{48^{2}-4\times 5\left(-91\right)}}{2\times 5}$$

48 kvadratini chiqarish.

$$x=\frac{-48±\sqrt{2304-4\times 5\left(-91\right)}}{2\times 5}$$

-4 ni 5 marotabaga ko'paytirish.

$$x=\frac{-48±\sqrt{2304-20\left(-91\right)}}{2\times 5}$$

-20 ni -91 marotabaga ko'paytirish.

$$x=\frac{-48±\sqrt{2304+1820}}{2\times 5}$$

2304 ni 1820 ga qo'shish.

$$x=\frac{-48±\sqrt{4124}}{2\times 5}$$

4124 ning kvadrat ildizini chiqarish.

$$x=\frac{-48±2\sqrt{1031}}{2\times 5}$$

2 ni 5 marotabaga ko'paytirish.

$$x=\frac{-48±2\sqrt{1031}}{10}$$

x=\frac{-48±2\sqrt{1031}}{10} tenglamasini yeching, bunda ± musbat. -48 ni 2\sqrt{1031} ga qo'shish.

$$x=\frac{2\sqrt{1031}-48}{10}$$

-48+2\sqrt{1031} ni 10 ga bo'lish.

$$x=\frac{\sqrt{1031}-24}{5}$$

x=\frac{-48±2\sqrt{1031}}{10} tenglamasini yeching, bunda ± manfiy. -48 dan 2\sqrt{1031} ni ayirish.

$$x=\frac{-2\sqrt{1031}-48}{10}$$

-48-2\sqrt{1031} ni 10 ga bo'lish.

$$x=\frac{-\sqrt{1031}-24}{5}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{-24+\sqrt{1031}}{5} ga va x_{2} uchun \frac{-24-\sqrt{1031}}{5} ga bo‘ling.

$$5x^{2}+48x-91=5\left(x-\frac{\sqrt{1031}-24}{5}\right)\left(x-\frac{-\sqrt{1031}-24}{5}\right)$$

Baholash

$$5x^{2}+48x-91$$