-20x^2+66x-20 eching

$$-20 { x }^{ 2 } +66x-20$$

Omil

$$-20\left(x-\frac{33-\sqrt{689}}{20}\right)\left(x-\frac{\sqrt{689}+33}{20}\right)$$

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.

$$-20x^{2}+66x-20=0$$

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.

$$x=\frac{-66±\sqrt{66^{2}-4\left(-20\right)\left(-20\right)}}{2\left(-20\right)}$$

66 kvadratini chiqarish.

$$x=\frac{-66±\sqrt{4356-4\left(-20\right)\left(-20\right)}}{2\left(-20\right)}$$

-4 ni -20 marotabaga ko'paytirish.

$$x=\frac{-66±\sqrt{4356+80\left(-20\right)}}{2\left(-20\right)}$$

80 ni -20 marotabaga ko'paytirish.

$$x=\frac{-66±\sqrt{4356-1600}}{2\left(-20\right)}$$

4356 ni -1600 ga qo'shish.

$$x=\frac{-66±\sqrt{2756}}{2\left(-20\right)}$$

2756 ning kvadrat ildizini chiqarish.

$$x=\frac{-66±2\sqrt{689}}{2\left(-20\right)}$$

2 ni -20 marotabaga ko'paytirish.

$$x=\frac{-66±2\sqrt{689}}{-40}$$

x=\frac{-66±2\sqrt{689}}{-40} tenglamasini yeching, bunda ± musbat. -66 ni 2\sqrt{689} ga qo'shish.

$$x=\frac{2\sqrt{689}-66}{-40}$$

-66+2\sqrt{689} ni -40 ga bo'lish.

$$x=\frac{33-\sqrt{689}}{20}$$

x=\frac{-66±2\sqrt{689}}{-40} tenglamasini yeching, bunda ± manfiy. -66 dan 2\sqrt{689} ni ayirish.

$$x=\frac{-2\sqrt{689}-66}{-40}$$

-66-2\sqrt{689} ni -40 ga bo'lish.

$$x=\frac{\sqrt{689}+33}{20}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{33-\sqrt{689}}{20} ga va x_{2} uchun \frac{33+\sqrt{689}}{20} ga bo‘ling.

$$-20x^{2}+66x-20=-20\left(x-\frac{33-\sqrt{689}}{20}\right)\left(x-\frac{\sqrt{689}+33}{20}\right)$$

Baholash

$$-20x^{2}+66x-20$$