(x^2+16x+16)-25 eching

$$( { x }^{ 2 } +16x+16)-25$$

Omil

$$\left(x-\left(-\sqrt{73}-8\right)\right)\left(x-\left(\sqrt{73}-8\right)\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

-9 olish uchun 16 dan 25 ni ayirish.

$$factor(x^{2}+16x-9)$$

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.

$$x^{2}+16x-9=0$$

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.

$$x=\frac{-16±\sqrt{16^{2}-4\left(-9\right)}}{2}$$

16 kvadratini chiqarish.

$$x=\frac{-16±\sqrt{256-4\left(-9\right)}}{2}$$

-4 ni -9 marotabaga ko'paytirish.

$$x=\frac{-16±\sqrt{256+36}}{2}$$

256 ni 36 ga qo'shish.

$$x=\frac{-16±\sqrt{292}}{2}$$

292 ning kvadrat ildizini chiqarish.

$$x=\frac{-16±2\sqrt{73}}{2}$$

x=\frac{-16±2\sqrt{73}}{2} tenglamasini yeching, bunda ± musbat. -16 ni 2\sqrt{73} ga qo'shish.

$$x=\frac{2\sqrt{73}-16}{2}$$

-16+2\sqrt{73} ni 2 ga bo'lish.

$$x=\sqrt{73}-8$$

x=\frac{-16±2\sqrt{73}}{2} tenglamasini yeching, bunda ± manfiy. -16 dan 2\sqrt{73} ni ayirish.

$$x=\frac{-2\sqrt{73}-16}{2}$$

-16-2\sqrt{73} ni 2 ga bo'lish.

$$x=-\sqrt{73}-8$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun -8+\sqrt{73} ga va x_{2} uchun -8-\sqrt{73} ga bo‘ling.

$$x^{2}+16x-9=\left(x-\left(\sqrt{73}-8\right)\right)\left(x-\left(-\sqrt{73}-8\right)\right)$$

Baholash

$$x^{2}+16x-9$$

Yechim qadamlari

-9 olish uchun 16 dan 25 ni ayirish.

$$x^{2}+16x-9$$