108+x^2/4=x^2 eching

$$\frac { 108 + x ^ { 2 } } { 4 } = x ^ { 2 }$$

x uchun yechish

$$x=6$$

$$x=-6$$

Kvadrat ildizini topish bo'yicha qadamlar

Tenglamaning ikkala tarafini 4 ga ko'paytirish.

$$108+x^{2}=4x^{2}$$

Ikkala tarafdan 4x^{2} ni ayirish.

$$108+x^{2}-4x^{2}=0$$

-3x^{2} ni olish uchun x^{2} va -4x^{2} ni birlashtirish.

$$108-3x^{2}=0$$

Ikkala tarafdan 108 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-3x^{2}=-108$$

Ikki tarafini -3 ga bo‘ling.

$$x^{2}=\frac{-108}{-3}$$

36 ni olish uchun -108 ni -3 ga bo‘ling.

$$x^{2}=36$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=6 x=-6$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tenglamaning ikkala tarafini 4 ga ko'paytirish.

$$108+x^{2}=4x^{2}$$

Ikkala tarafdan 4x^{2} ni ayirish.

$$108+x^{2}-4x^{2}=0$$

-3x^{2} ni olish uchun x^{2} va -4x^{2} ni birlashtirish.

$$108-3x^{2}=0$$

Bu kabi kvadrat tenglamalarni x^{2} sharti bilan, biroq x shartisiz hamon kvadrat tenglamasidan foydalanib yechish mumkin, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ular standart formulaga solingandan so'ng: ax^{2}+bx+c=0.

$$-3x^{2}+108=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -3 ni a, 0 ni b va 108 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-3\right)\times 108}}{2\left(-3\right)}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-3\right)\times 108}}{2\left(-3\right)}$$

-4 ni -3 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{12\times 108}}{2\left(-3\right)}$$

12 ni 108 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{1296}}{2\left(-3\right)}$$

1296 ning kvadrat ildizini chiqarish.

$$x=\frac{0±36}{2\left(-3\right)}$$

2 ni -3 marotabaga ko'paytirish.

$$x=\frac{0±36}{-6}$$

x=\frac{0±36}{-6} tenglamasini yeching, bunda ± musbat. 36 ni -6 ga bo'lish.

$$x=-6$$

x=\frac{0±36}{-6} tenglamasini yeching, bunda ± manfiy. -36 ni -6 ga bo'lish.

$$x=6$$

Tenglama yechildi.

$$x=-6 x=6$$