-4x^2-8x+4 eching

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

Omil

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

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.

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

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.

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

-8 kvadratini chiqarish.

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

-4 ni -4 marotabaga ko'paytirish.

$$x=\frac{-\left(-8\right)±\sqrt{64+16\times 4}}{2\left(-4\right)}$$

16 ni 4 marotabaga ko'paytirish.

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

64 ni 64 ga qo'shish.

$$x=\frac{-\left(-8\right)±\sqrt{128}}{2\left(-4\right)}$$

128 ning kvadrat ildizini chiqarish.

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

-8 ning teskarisi 8 ga teng.

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

2 ni -4 marotabaga ko'paytirish.

$$x=\frac{8±8\sqrt{2}}{-8}$$

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

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

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

$$x=-\left(\sqrt{2}+1\right)$$

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

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

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

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

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

$$-4x^{2}-8x+4=-4\left(x-\left(-\left(\sqrt{2}+1\right)\right)\right)\left(x-\left(\sqrt{2}-1\right)\right)$$

Baholash

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