3x^2+4x-8-2x^2+4x+2 eching

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

Baholash

$$x^{2}+8x-6$$

Yechim qadamlari

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

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

8x ni olish uchun 4x va 4x ni birlashtirish.

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

-6 olish uchun -8 va 2'ni qo'shing.

$$x^{2}+8x-6$$

Omil

$$\left(x-\left(-\sqrt{22}-4\right)\right)\left(x-\left(\sqrt{22}-4\right)\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

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

8x ni olish uchun 4x va 4x ni birlashtirish.

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

-6 olish uchun -8 va 2'ni qo'shing.

$$factor(x^{2}+8x-6)$$

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.

$$x^{2}+8x-6=0$$

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.

$$x=\frac{-8±\sqrt{8^{2}-4\left(-6\right)}}{2}$$

8 kvadratini chiqarish.

$$x=\frac{-8±\sqrt{64-4\left(-6\right)}}{2}$$

-4 ni -6 marotabaga ko'paytirish.

$$x=\frac{-8±\sqrt{64+24}}{2}$$

64 ni 24 ga qo'shish.

$$x=\frac{-8±\sqrt{88}}{2}$$

88 ning kvadrat ildizini chiqarish.

$$x=\frac{-8±2\sqrt{22}}{2}$$

x=\frac{-8±2\sqrt{22}}{2} tenglamasini yeching, bunda ± musbat. -8 ni 2\sqrt{22} ga qo'shish.

$$x=\frac{2\sqrt{22}-8}{2}$$

-8+2\sqrt{22} ni 2 ga bo'lish.

$$x=\sqrt{22}-4$$

x=\frac{-8±2\sqrt{22}}{2} tenglamasini yeching, bunda ± manfiy. -8 dan 2\sqrt{22} ni ayirish.

$$x=\frac{-2\sqrt{22}-8}{2}$$

-8-2\sqrt{22} ni 2 ga bo'lish.

$$x=-\sqrt{22}-4$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun -4+\sqrt{22} ga va x_{2} uchun -4-\sqrt{22} ga bo‘ling.

$$x^{2}+8x-6=\left(x-\left(\sqrt{22}-4\right)\right)\left(x-\left(-\sqrt{22}-4\right)\right)$$