x^2+3x-4x^2+7x+12 eching

$$x ^ { 2 } + 3 x - 4 x ^ { 2 } + 7 x + 12$$

Baholash

$$12+10x-3x^{2}$$

Yechim qadamlari

-3x^{2} ni olish uchun x^{2} va -4x^{2} ni birlashtirish.

$$-3x^{2}+3x+7x+12$$

10x ni olish uchun 3x va 7x ni birlashtirish.

$$-3x^{2}+10x+12$$

Omil

$$-3\left(x-\frac{5-\sqrt{61}}{3}\right)\left(x-\frac{\sqrt{61}+5}{3}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

-3x^{2} ni olish uchun x^{2} va -4x^{2} ni birlashtirish.

$$factor(-3x^{2}+3x+7x+12)$$

10x ni olish uchun 3x va 7x ni birlashtirish.

$$factor(-3x^{2}+10x+12)$$

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.

$$-3x^{2}+10x+12=0$$

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.

$$x=\frac{-10±\sqrt{10^{2}-4\left(-3\right)\times 12}}{2\left(-3\right)}$$

10 kvadratini chiqarish.

$$x=\frac{-10±\sqrt{100-4\left(-3\right)\times 12}}{2\left(-3\right)}$$

-4 ni -3 marotabaga ko'paytirish.

$$x=\frac{-10±\sqrt{100+12\times 12}}{2\left(-3\right)}$$

12 ni 12 marotabaga ko'paytirish.

$$x=\frac{-10±\sqrt{100+144}}{2\left(-3\right)}$$

100 ni 144 ga qo'shish.

$$x=\frac{-10±\sqrt{244}}{2\left(-3\right)}$$

244 ning kvadrat ildizini chiqarish.

$$x=\frac{-10±2\sqrt{61}}{2\left(-3\right)}$$

2 ni -3 marotabaga ko'paytirish.

$$x=\frac{-10±2\sqrt{61}}{-6}$$

x=\frac{-10±2\sqrt{61}}{-6} tenglamasini yeching, bunda ± musbat. -10 ni 2\sqrt{61} ga qo'shish.

$$x=\frac{2\sqrt{61}-10}{-6}$$

-10+2\sqrt{61} ni -6 ga bo'lish.

$$x=\frac{5-\sqrt{61}}{3}$$

x=\frac{-10±2\sqrt{61}}{-6} tenglamasini yeching, bunda ± manfiy. -10 dan 2\sqrt{61} ni ayirish.

$$x=\frac{-2\sqrt{61}-10}{-6}$$

-10-2\sqrt{61} ni -6 ga bo'lish.

$$x=\frac{\sqrt{61}+5}{3}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{5-\sqrt{61}}{3} ga va x_{2} uchun \frac{5+\sqrt{61}}{3} ga bo‘ling.

$$-3x^{2}+10x+12=-3\left(x-\frac{5-\sqrt{61}}{3}\right)\left(x-\frac{\sqrt{61}+5}{3}\right)$$