f(x)=-16x^2+14x+10 eching

$$f ( x ) = - 16 x ^ { 2 } + 14 x + 10$$

Omil

$$-16\left(x-\frac{7-\sqrt{209}}{16}\right)\left(x-\frac{\sqrt{209}+7}{16}\right)$$

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.

$$-16x^{2}+14x+10=0$$

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.

$$x=\frac{-14±\sqrt{14^{2}-4\left(-16\right)\times 10}}{2\left(-16\right)}$$

14 kvadratini chiqarish.

$$x=\frac{-14±\sqrt{196-4\left(-16\right)\times 10}}{2\left(-16\right)}$$

-4 ni -16 marotabaga ko'paytirish.

$$x=\frac{-14±\sqrt{196+64\times 10}}{2\left(-16\right)}$$

64 ni 10 marotabaga ko'paytirish.

$$x=\frac{-14±\sqrt{196+640}}{2\left(-16\right)}$$

196 ni 640 ga qo'shish.

$$x=\frac{-14±\sqrt{836}}{2\left(-16\right)}$$

836 ning kvadrat ildizini chiqarish.

$$x=\frac{-14±2\sqrt{209}}{2\left(-16\right)}$$

2 ni -16 marotabaga ko'paytirish.

$$x=\frac{-14±2\sqrt{209}}{-32}$$

x=\frac{-14±2\sqrt{209}}{-32} tenglamasini yeching, bunda ± musbat. -14 ni 2\sqrt{209} ga qo'shish.

$$x=\frac{2\sqrt{209}-14}{-32}$$

-14+2\sqrt{209} ni -32 ga bo'lish.

$$x=\frac{7-\sqrt{209}}{16}$$

x=\frac{-14±2\sqrt{209}}{-32} tenglamasini yeching, bunda ± manfiy. -14 dan 2\sqrt{209} ni ayirish.

$$x=\frac{-2\sqrt{209}-14}{-32}$$

-14-2\sqrt{209} ni -32 ga bo'lish.

$$x=\frac{\sqrt{209}+7}{16}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{7-\sqrt{209}}{16} ga va x_{2} uchun \frac{7+\sqrt{209}}{16} ga bo‘ling.

$$-16x^{2}+14x+10=-16\left(x-\frac{7-\sqrt{209}}{16}\right)\left(x-\frac{\sqrt{209}+7}{16}\right)$$

Baholash

$$10+14x-16x^{2}$$