8x^2-14=-11 eching

$$8 x ^ { 2 } - 14 = - 11$$

x uchun yechish

$$x=\frac{\sqrt{6}}{4}\approx 0,612372436$$

$$x=-\frac{\sqrt{6}}{4}\approx -0,612372436$$

Kvadrat ildizini topish bo'yicha qadamlar

14 ni ikki tarafga qo’shing.

$$8x^{2}=-11+14$$

3 olish uchun -11 va 14'ni qo'shing.

$$8x^{2}=3$$

Ikki tarafini 8 ga bo‘ling.

$$x^{2}=\frac{3}{8}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{\sqrt{6}}{4} x=-\frac{\sqrt{6}}{4}$$

Kvadrat tenglamalaridan foydalanish qoidalari

11 ni ikki tarafga qo’shing.

$$8x^{2}-14+11=0$$

-3 olish uchun -14 va 11'ni qo'shing.

$$8x^{2}-3=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 8 ni a, 0 ni b va -3 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 8\left(-3\right)}}{2\times 8}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 8\left(-3\right)}}{2\times 8}$$

-4 ni 8 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-32\left(-3\right)}}{2\times 8}$$

-32 ni -3 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{96}}{2\times 8}$$

96 ning kvadrat ildizini chiqarish.

$$x=\frac{0±4\sqrt{6}}{2\times 8}$$

2 ni 8 marotabaga ko'paytirish.

$$x=\frac{0±4\sqrt{6}}{16}$$

x=\frac{0±4\sqrt{6}}{16} tenglamasini yeching, bunda ± musbat.

$$x=\frac{\sqrt{6}}{4}$$

x=\frac{0±4\sqrt{6}}{16} tenglamasini yeching, bunda ± manfiy.

$$x=-\frac{\sqrt{6}}{4}$$

Tenglama yechildi.

$$x=\frac{\sqrt{6}}{4} x=-\frac{\sqrt{6}}{4}$$