11x^2-54x-192 eching

$$11 { x }^{ 2 } -54x-192$$

Omil

$$11\left(x-\frac{27-\sqrt{2841}}{11}\right)\left(x-\frac{\sqrt{2841}+27}{11}\right)$$

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.

$$11x^{2}-54x-192=0$$

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.

$$x=\frac{-\left(-54\right)±\sqrt{\left(-54\right)^{2}-4\times 11\left(-192\right)}}{2\times 11}$$

-54 kvadratini chiqarish.

$$x=\frac{-\left(-54\right)±\sqrt{2916-4\times 11\left(-192\right)}}{2\times 11}$$

-4 ni 11 marotabaga ko'paytirish.

$$x=\frac{-\left(-54\right)±\sqrt{2916-44\left(-192\right)}}{2\times 11}$$

-44 ni -192 marotabaga ko'paytirish.

$$x=\frac{-\left(-54\right)±\sqrt{2916+8448}}{2\times 11}$$

2916 ni 8448 ga qo'shish.

$$x=\frac{-\left(-54\right)±\sqrt{11364}}{2\times 11}$$

11364 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-54\right)±2\sqrt{2841}}{2\times 11}$$

-54 ning teskarisi 54 ga teng.

$$x=\frac{54±2\sqrt{2841}}{2\times 11}$$

2 ni 11 marotabaga ko'paytirish.

$$x=\frac{54±2\sqrt{2841}}{22}$$

x=\frac{54±2\sqrt{2841}}{22} tenglamasini yeching, bunda ± musbat. 54 ni 2\sqrt{2841} ga qo'shish.

$$x=\frac{2\sqrt{2841}+54}{22}$$

54+2\sqrt{2841} ni 22 ga bo'lish.

$$x=\frac{\sqrt{2841}+27}{11}$$

x=\frac{54±2\sqrt{2841}}{22} tenglamasini yeching, bunda ± manfiy. 54 dan 2\sqrt{2841} ni ayirish.

$$x=\frac{54-2\sqrt{2841}}{22}$$

54-2\sqrt{2841} ni 22 ga bo'lish.

$$x=\frac{27-\sqrt{2841}}{11}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{27+\sqrt{2841}}{11} ga va x_{2} uchun \frac{27-\sqrt{2841}}{11} ga bo‘ling.

$$11x^{2}-54x-192=11\left(x-\frac{\sqrt{2841}+27}{11}\right)\left(x-\frac{27-\sqrt{2841}}{11}\right)$$

Baholash

$$11x^{2}-54x-192$$