18x^2+32x-16 eching

$$18 { x }^{ 2 } +32x-16$$

Omil

$$18\left(x-\frac{-2\sqrt{34}-8}{9}\right)\left(x-\frac{2\sqrt{34}-8}{9}\right)$$

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.

$$18x^{2}+32x-16=0$$

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.

$$x=\frac{-32±\sqrt{32^{2}-4\times 18\left(-16\right)}}{2\times 18}$$

32 kvadratini chiqarish.

$$x=\frac{-32±\sqrt{1024-4\times 18\left(-16\right)}}{2\times 18}$$

-4 ni 18 marotabaga ko'paytirish.

$$x=\frac{-32±\sqrt{1024-72\left(-16\right)}}{2\times 18}$$

-72 ni -16 marotabaga ko'paytirish.

$$x=\frac{-32±\sqrt{1024+1152}}{2\times 18}$$

1024 ni 1152 ga qo'shish.

$$x=\frac{-32±\sqrt{2176}}{2\times 18}$$

2176 ning kvadrat ildizini chiqarish.

$$x=\frac{-32±8\sqrt{34}}{2\times 18}$$

2 ni 18 marotabaga ko'paytirish.

$$x=\frac{-32±8\sqrt{34}}{36}$$

x=\frac{-32±8\sqrt{34}}{36} tenglamasini yeching, bunda ± musbat. -32 ni 8\sqrt{34} ga qo'shish.

$$x=\frac{8\sqrt{34}-32}{36}$$

-32+8\sqrt{34} ni 36 ga bo'lish.

$$x=\frac{2\sqrt{34}-8}{9}$$

x=\frac{-32±8\sqrt{34}}{36} tenglamasini yeching, bunda ± manfiy. -32 dan 8\sqrt{34} ni ayirish.

$$x=\frac{-8\sqrt{34}-32}{36}$$

-32-8\sqrt{34} ni 36 ga bo'lish.

$$x=\frac{-2\sqrt{34}-8}{9}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{-8+2\sqrt{34}}{9} ga va x_{2} uchun \frac{-8-2\sqrt{34}}{9} ga bo‘ling.

$$18x^{2}+32x-16=18\left(x-\frac{2\sqrt{34}-8}{9}\right)\left(x-\frac{-2\sqrt{34}-8}{9}\right)$$

Baholash

$$18x^{2}+32x-16$$