16x^2-4x-21 eching

$$16 x ^ { 2 } - 4 x - 21$$

Omil

$$16\left(x-\frac{1-\sqrt{85}}{8}\right)\left(x-\frac{\sqrt{85}+1}{8}\right)$$

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.

$$16x^{2}-4x-21=0$$

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.

$$x=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\times 16\left(-21\right)}}{2\times 16}$$

-4 kvadratini chiqarish.

$$x=\frac{-\left(-4\right)±\sqrt{16-4\times 16\left(-21\right)}}{2\times 16}$$

-4 ni 16 marotabaga ko'paytirish.

$$x=\frac{-\left(-4\right)±\sqrt{16-64\left(-21\right)}}{2\times 16}$$

-64 ni -21 marotabaga ko'paytirish.

$$x=\frac{-\left(-4\right)±\sqrt{16+1344}}{2\times 16}$$

16 ni 1344 ga qo'shish.

$$x=\frac{-\left(-4\right)±\sqrt{1360}}{2\times 16}$$

1360 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-4\right)±4\sqrt{85}}{2\times 16}$$

-4 ning teskarisi 4 ga teng.

$$x=\frac{4±4\sqrt{85}}{2\times 16}$$

2 ni 16 marotabaga ko'paytirish.

$$x=\frac{4±4\sqrt{85}}{32}$$

x=\frac{4±4\sqrt{85}}{32} tenglamasini yeching, bunda ± musbat. 4 ni 4\sqrt{85} ga qo'shish.

$$x=\frac{4\sqrt{85}+4}{32}$$

4+4\sqrt{85} ni 32 ga bo'lish.

$$x=\frac{\sqrt{85}+1}{8}$$

x=\frac{4±4\sqrt{85}}{32} tenglamasini yeching, bunda ± manfiy. 4 dan 4\sqrt{85} ni ayirish.

$$x=\frac{4-4\sqrt{85}}{32}$$

4-4\sqrt{85} ni 32 ga bo'lish.

$$x=\frac{1-\sqrt{85}}{8}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{1+\sqrt{85}}{8} ga va x_{2} uchun \frac{1-\sqrt{85}}{8} ga bo‘ling.

$$16x^{2}-4x-21=16\left(x-\frac{\sqrt{85}+1}{8}\right)\left(x-\frac{1-\sqrt{85}}{8}\right)$$

Baholash

$$16x^{2}-4x-21$$