3x^2+72x-55 eching

$$3 x ^ { 2 } + 72 x - 55$$

Omil

$$3\left(x-\left(-\frac{\sqrt{1461}}{3}-12\right)\right)\left(x-\left(\frac{\sqrt{1461}}{3}-12\right)\right)$$

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.

$$3x^{2}+72x-55=0$$

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.

$$x=\frac{-72±\sqrt{72^{2}-4\times 3\left(-55\right)}}{2\times 3}$$

72 kvadratini chiqarish.

$$x=\frac{-72±\sqrt{5184-4\times 3\left(-55\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-72±\sqrt{5184-12\left(-55\right)}}{2\times 3}$$

-12 ni -55 marotabaga ko'paytirish.

$$x=\frac{-72±\sqrt{5184+660}}{2\times 3}$$

5184 ni 660 ga qo'shish.

$$x=\frac{-72±\sqrt{5844}}{2\times 3}$$

5844 ning kvadrat ildizini chiqarish.

$$x=\frac{-72±2\sqrt{1461}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{-72±2\sqrt{1461}}{6}$$

x=\frac{-72±2\sqrt{1461}}{6} tenglamasini yeching, bunda ± musbat. -72 ni 2\sqrt{1461} ga qo'shish.

$$x=\frac{2\sqrt{1461}-72}{6}$$

-72+2\sqrt{1461} ni 6 ga bo'lish.

$$x=\frac{\sqrt{1461}}{3}-12$$

x=\frac{-72±2\sqrt{1461}}{6} tenglamasini yeching, bunda ± manfiy. -72 dan 2\sqrt{1461} ni ayirish.

$$x=\frac{-2\sqrt{1461}-72}{6}$$

-72-2\sqrt{1461} ni 6 ga bo'lish.

$$x=-\frac{\sqrt{1461}}{3}-12$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun -12+\frac{\sqrt{1461}}{3} ga va x_{2} uchun -12-\frac{\sqrt{1461}}{3} ga bo‘ling.

$$3x^{2}+72x-55=3\left(x-\left(\frac{\sqrt{1461}}{3}-12\right)\right)\left(x-\left(-\frac{\sqrt{1461}}{3}-12\right)\right)$$

Baholash

$$3x^{2}+72x-55$$