x(x+2)=(x+3)(x-3)=13 eching

$$x ( x + 2 ) = ( x + 3 ) ( x - 3 ) = 13$$

x uchun yechish

$$x=\sqrt{22}\approx 4,69041576$$

$$x=-\sqrt{22}\approx -4,69041576$$

Kvadrat ildizini topish bo'yicha qadamlar

Hisoblang: \left(x+3\right)\left(x-3\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 3 kvadratini chiqarish.

$$x^{2}-9=13$$

9 ni ikki tarafga qo’shing.

$$x^{2}=13+9$$

22 olish uchun 13 va 9'ni qo'shing.

$$x^{2}=22$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\sqrt{22} x=-\sqrt{22}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Hisoblang: \left(x+3\right)\left(x-3\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 3 kvadratini chiqarish.

$$x^{2}-9=13$$

Ikkala tarafdan 13 ni ayirish.

$$x^{2}-9-13=0$$

-22 olish uchun -9 dan 13 ni ayirish.

$$x^{2}-22=0$$

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 -22 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-22\right)}}{2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-22\right)}}{2}$$

-4 ni -22 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{88}}{2}$$

88 ning kvadrat ildizini chiqarish.

$$x=\frac{0±2\sqrt{22}}{2}$$

x=\frac{0±2\sqrt{22}}{2} tenglamasini yeching, bunda ± musbat.

$$x=\sqrt{22}$$

x=\frac{0±2\sqrt{22}}{2} tenglamasini yeching, bunda ± manfiy.

$$x=-\sqrt{22}$$

Tenglama yechildi.

$$x=\sqrt{22} x=-\sqrt{22}$$