5x^2+3x-100 eching

$$5 x ^ { 2 } + 3 x - 100$$

Omil

$$5\left(x-\frac{-7\sqrt{41}-3}{10}\right)\left(x-\frac{7\sqrt{41}-3}{10}\right)$$

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.

$$5x^{2}+3x-100=0$$

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.

$$x=\frac{-3±\sqrt{3^{2}-4\times 5\left(-100\right)}}{2\times 5}$$

3 kvadratini chiqarish.

$$x=\frac{-3±\sqrt{9-4\times 5\left(-100\right)}}{2\times 5}$$

-4 ni 5 marotabaga ko'paytirish.

$$x=\frac{-3±\sqrt{9-20\left(-100\right)}}{2\times 5}$$

-20 ni -100 marotabaga ko'paytirish.

$$x=\frac{-3±\sqrt{9+2000}}{2\times 5}$$

9 ni 2000 ga qo'shish.

$$x=\frac{-3±\sqrt{2009}}{2\times 5}$$

2009 ning kvadrat ildizini chiqarish.

$$x=\frac{-3±7\sqrt{41}}{2\times 5}$$

2 ni 5 marotabaga ko'paytirish.

$$x=\frac{-3±7\sqrt{41}}{10}$$

x=\frac{-3±7\sqrt{41}}{10} tenglamasini yeching, bunda ± musbat. -3 ni 7\sqrt{41} ga qo'shish.

$$x=\frac{7\sqrt{41}-3}{10}$$

x=\frac{-3±7\sqrt{41}}{10} tenglamasini yeching, bunda ± manfiy. -3 dan 7\sqrt{41} ni ayirish.

$$x=\frac{-7\sqrt{41}-3}{10}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{-3+7\sqrt{41}}{10} ga va x_{2} uchun \frac{-3-7\sqrt{41}}{10} ga bo‘ling.

$$5x^{2}+3x-100=5\left(x-\frac{7\sqrt{41}-3}{10}\right)\left(x-\frac{-7\sqrt{41}-3}{10}\right)$$

Baholash

$$5x^{2}+3x-100$$