x^2-4x^2+4+8x eching

$$x ^ { 2 } - 4 x ^ { 2 } + 4 + 8 x$$

Omil

$$-3\left(x-\frac{4-2\sqrt{7}}{3}\right)\left(x-\frac{2\sqrt{7}+4}{3}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$factor(-3x^{2}+4+8x)$$

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.

$$-3x^{2}+8x+4=0$$

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.

$$x=\frac{-8±\sqrt{8^{2}-4\left(-3\right)\times 4}}{2\left(-3\right)}$$

8 kvadratini chiqarish.

$$x=\frac{-8±\sqrt{64-4\left(-3\right)\times 4}}{2\left(-3\right)}$$

-4 ni -3 marotabaga ko'paytirish.

$$x=\frac{-8±\sqrt{64+12\times 4}}{2\left(-3\right)}$$

12 ni 4 marotabaga ko'paytirish.

$$x=\frac{-8±\sqrt{64+48}}{2\left(-3\right)}$$

64 ni 48 ga qo'shish.

$$x=\frac{-8±\sqrt{112}}{2\left(-3\right)}$$

112 ning kvadrat ildizini chiqarish.

$$x=\frac{-8±4\sqrt{7}}{2\left(-3\right)}$$

2 ni -3 marotabaga ko'paytirish.

$$x=\frac{-8±4\sqrt{7}}{-6}$$

x=\frac{-8±4\sqrt{7}}{-6} tenglamasini yeching, bunda ± musbat. -8 ni 4\sqrt{7} ga qo'shish.

$$x=\frac{4\sqrt{7}-8}{-6}$$

-8+4\sqrt{7} ni -6 ga bo'lish.

$$x=\frac{4-2\sqrt{7}}{3}$$

x=\frac{-8±4\sqrt{7}}{-6} tenglamasini yeching, bunda ± manfiy. -8 dan 4\sqrt{7} ni ayirish.

$$x=\frac{-4\sqrt{7}-8}{-6}$$

-8-4\sqrt{7} ni -6 ga bo'lish.

$$x=\frac{2\sqrt{7}+4}{3}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{4-2\sqrt{7}}{3} ga va x_{2} uchun \frac{4+2\sqrt{7}}{3} ga bo‘ling.

$$-3x^{2}+8x+4=-3\left(x-\frac{4-2\sqrt{7}}{3}\right)\left(x-\frac{2\sqrt{7}+4}{3}\right)$$

Baholash

$$4+8x-3x^{2}$$

Yechim qadamlari

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

$$-3x^{2}+4+8x$$