-x^2+16x-51 eching

$$- { x }^{ 2 } +16x-51$$

Omil

$$-\left(x-\left(8-\sqrt{13}\right)\right)\left(x-\left(\sqrt{13}+8\right)\right)$$

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.

$$-x^{2}+16x-51=0$$

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.

$$x=\frac{-16±\sqrt{16^{2}-4\left(-1\right)\left(-51\right)}}{2\left(-1\right)}$$

16 kvadratini chiqarish.

$$x=\frac{-16±\sqrt{256-4\left(-1\right)\left(-51\right)}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-16±\sqrt{256+4\left(-51\right)}}{2\left(-1\right)}$$

4 ni -51 marotabaga ko'paytirish.

$$x=\frac{-16±\sqrt{256-204}}{2\left(-1\right)}$$

256 ni -204 ga qo'shish.

$$x=\frac{-16±\sqrt{52}}{2\left(-1\right)}$$

52 ning kvadrat ildizini chiqarish.

$$x=\frac{-16±2\sqrt{13}}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{-16±2\sqrt{13}}{-2}$$

x=\frac{-16±2\sqrt{13}}{-2} tenglamasini yeching, bunda ± musbat. -16 ni 2\sqrt{13} ga qo'shish.

$$x=\frac{2\sqrt{13}-16}{-2}$$

-16+2\sqrt{13} ni -2 ga bo'lish.

$$x=8-\sqrt{13}$$

x=\frac{-16±2\sqrt{13}}{-2} tenglamasini yeching, bunda ± manfiy. -16 dan 2\sqrt{13} ni ayirish.

$$x=\frac{-2\sqrt{13}-16}{-2}$$

-16-2\sqrt{13} ni -2 ga bo'lish.

$$x=\sqrt{13}+8$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 8-\sqrt{13} ga va x_{2} uchun 8+\sqrt{13} ga bo‘ling.

$$-x^{2}+16x-51=-\left(x-\left(8-\sqrt{13}\right)\right)\left(x-\left(\sqrt{13}+8\right)\right)$$

Baholash

$$-x^{2}+16x-51$$