2x^2+4-6x^2+4x+6 eching

$$2 { x }^{ 2 } +4-6 { x }^{ 2 } +4x+6$$

Baholash

$$10+4x-4x^{2}$$

Yechim qadamlari

-4x^{2} ni olish uchun 2x^{2} va -6x^{2} ni birlashtirish.

$$-4x^{2}+4+4x+6$$

10 olish uchun 4 va 6'ni qo'shing.

$$-4x^{2}+10+4x$$

Omil

$$-4\left(x-\frac{1-\sqrt{11}}{2}\right)\left(x-\frac{\sqrt{11}+1}{2}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

-4x^{2} ni olish uchun 2x^{2} va -6x^{2} ni birlashtirish.

$$factor(-4x^{2}+4+4x+6)$$

10 olish uchun 4 va 6'ni qo'shing.

$$factor(-4x^{2}+10+4x)$$

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.

$$-4x^{2}+4x+10=0$$

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.

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

4 kvadratini chiqarish.

$$x=\frac{-4±\sqrt{16-4\left(-4\right)\times 10}}{2\left(-4\right)}$$

-4 ni -4 marotabaga ko'paytirish.

$$x=\frac{-4±\sqrt{16+16\times 10}}{2\left(-4\right)}$$

16 ni 10 marotabaga ko'paytirish.

$$x=\frac{-4±\sqrt{16+160}}{2\left(-4\right)}$$

16 ni 160 ga qo'shish.

$$x=\frac{-4±\sqrt{176}}{2\left(-4\right)}$$

176 ning kvadrat ildizini chiqarish.

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

2 ni -4 marotabaga ko'paytirish.

$$x=\frac{-4±4\sqrt{11}}{-8}$$

x=\frac{-4±4\sqrt{11}}{-8} tenglamasini yeching, bunda ± musbat. -4 ni 4\sqrt{11} ga qo'shish.

$$x=\frac{4\sqrt{11}-4}{-8}$$

-4+4\sqrt{11} ni -8 ga bo'lish.

$$x=\frac{1-\sqrt{11}}{2}$$

x=\frac{-4±4\sqrt{11}}{-8} tenglamasini yeching, bunda ± manfiy. -4 dan 4\sqrt{11} ni ayirish.

$$x=\frac{-4\sqrt{11}-4}{-8}$$

-4-4\sqrt{11} ni -8 ga bo'lish.

$$x=\frac{\sqrt{11}+1}{2}$$

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

$$-4x^{2}+4x+10=-4\left(x-\frac{1-\sqrt{11}}{2}\right)\left(x-\frac{\sqrt{11}+1}{2}\right)$$