x^2-9=160 eching

$${ x }^{ 2 } -9=160$$

x uchun yechish

$$x=13$$

$$x=-13$$

Kvadratlar farqidan foydalangan qadamlar

Ikkala tarafdan 160 ni ayirish.

$$x^{2}-9-160=0$$

-169 olish uchun -9 dan 160 ni ayirish.

$$x^{2}-169=0$$

Hisoblang: x^{2}-169. x^{2}-169 ni x^{2}-13^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-13\right)\left(x+13\right)=0$$

Tenglamani yechish uchun x-13=0 va x+13=0 ni yeching.

$$x=13 x=-13$$

Kvadrat ildizini topish bo'yicha qadamlar

9 ni ikki tarafga qo’shing.

$$x^{2}=160+9$$

169 olish uchun 160 va 9'ni qo'shing.

$$x^{2}=169$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=13 x=-13$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 160 ni ayirish.

$$x^{2}-9-160=0$$

-169 olish uchun -9 dan 160 ni ayirish.

$$x^{2}-169=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 0 ni b va -169 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-169\right)}}{2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-169\right)}}{2}$$

-4 ni -169 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{676}}{2}$$

676 ning kvadrat ildizini chiqarish.

$$x=\frac{0±26}{2}$$

x=\frac{0±26}{2} tenglamasini yeching, bunda ± musbat. 26 ni 2 ga bo'lish.

$$x=13$$

x=\frac{0±26}{2} tenglamasini yeching, bunda ± manfiy. -26 ni 2 ga bo'lish.

$$x=-13$$

Tenglama yechildi.

$$x=13 x=-13$$