f(x)=8x^2+160x-4 eching

$$f ( x ) = 8 x ^ { 2 } + 160 x - 4$$

Omil

$$8\left(x-\left(-\frac{\sqrt{402}}{2}-10\right)\right)\left(x-\left(\frac{\sqrt{402}}{2}-10\right)\right)$$

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.

$$8x^{2}+160x-4=0$$

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.

$$x=\frac{-160±\sqrt{160^{2}-4\times 8\left(-4\right)}}{2\times 8}$$

160 kvadratini chiqarish.

$$x=\frac{-160±\sqrt{25600-4\times 8\left(-4\right)}}{2\times 8}$$

-4 ni 8 marotabaga ko'paytirish.

$$x=\frac{-160±\sqrt{25600-32\left(-4\right)}}{2\times 8}$$

-32 ni -4 marotabaga ko'paytirish.

$$x=\frac{-160±\sqrt{25600+128}}{2\times 8}$$

25600 ni 128 ga qo'shish.

$$x=\frac{-160±\sqrt{25728}}{2\times 8}$$

25728 ning kvadrat ildizini chiqarish.

$$x=\frac{-160±8\sqrt{402}}{2\times 8}$$

2 ni 8 marotabaga ko'paytirish.

$$x=\frac{-160±8\sqrt{402}}{16}$$

x=\frac{-160±8\sqrt{402}}{16} tenglamasini yeching, bunda ± musbat. -160 ni 8\sqrt{402} ga qo'shish.

$$x=\frac{8\sqrt{402}-160}{16}$$

-160+8\sqrt{402} ni 16 ga bo'lish.

$$x=\frac{\sqrt{402}}{2}-10$$

x=\frac{-160±8\sqrt{402}}{16} tenglamasini yeching, bunda ± manfiy. -160 dan 8\sqrt{402} ni ayirish.

$$x=\frac{-8\sqrt{402}-160}{16}$$

-160-8\sqrt{402} ni 16 ga bo'lish.

$$x=-\frac{\sqrt{402}}{2}-10$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun -10+\frac{\sqrt{402}}{2} ga va x_{2} uchun -10-\frac{\sqrt{402}}{2} ga bo‘ling.

$$8x^{2}+160x-4=8\left(x-\left(\frac{\sqrt{402}}{2}-10\right)\right)\left(x-\left(-\frac{\sqrt{402}}{2}-10\right)\right)$$

Baholash

$$8x^{2}+160x-4$$