quad205x^2+32x-21 eching

$$\quad 205 x ^ { 2 } + 32 x - 21$$

Omil

$$205\left(x-\frac{-\sqrt{4561}-16}{205}\right)\left(x-\frac{\sqrt{4561}-16}{205}\right)$$

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.

$$205x^{2}+32x-21=0$$

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.

$$x=\frac{-32±\sqrt{32^{2}-4\times 205\left(-21\right)}}{2\times 205}$$

32 kvadratini chiqarish.

$$x=\frac{-32±\sqrt{1024-4\times 205\left(-21\right)}}{2\times 205}$$

-4 ni 205 marotabaga ko'paytirish.

$$x=\frac{-32±\sqrt{1024-820\left(-21\right)}}{2\times 205}$$

-820 ni -21 marotabaga ko'paytirish.

$$x=\frac{-32±\sqrt{1024+17220}}{2\times 205}$$

1024 ni 17220 ga qo'shish.

$$x=\frac{-32±\sqrt{18244}}{2\times 205}$$

18244 ning kvadrat ildizini chiqarish.

$$x=\frac{-32±2\sqrt{4561}}{2\times 205}$$

2 ni 205 marotabaga ko'paytirish.

$$x=\frac{-32±2\sqrt{4561}}{410}$$

x=\frac{-32±2\sqrt{4561}}{410} tenglamasini yeching, bunda ± musbat. -32 ni 2\sqrt{4561} ga qo'shish.

$$x=\frac{2\sqrt{4561}-32}{410}$$

-32+2\sqrt{4561} ni 410 ga bo'lish.

$$x=\frac{\sqrt{4561}-16}{205}$$

x=\frac{-32±2\sqrt{4561}}{410} tenglamasini yeching, bunda ± manfiy. -32 dan 2\sqrt{4561} ni ayirish.

$$x=\frac{-2\sqrt{4561}-32}{410}$$

-32-2\sqrt{4561} ni 410 ga bo'lish.

$$x=\frac{-\sqrt{4561}-16}{205}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{-16+\sqrt{4561}}{205} ga va x_{2} uchun \frac{-16-\sqrt{4561}}{205} ga bo‘ling.

$$205x^{2}+32x-21=205\left(x-\frac{\sqrt{4561}-16}{205}\right)\left(x-\frac{-\sqrt{4561}-16}{205}\right)$$

Baholash

$$205x^{2}+32x-21$$