x^2-144=0 eching

$$x ^ { 2 } - 144 = 0$$

x uchun yechish

$$x=12$$

$$x=-12$$

Kvadratlar farqidan foydalangan qadamlar

Hisoblang: x^{2}-144. x^{2}-144 ni x^{2}-12^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-12\right)\left(x+12\right)=0$$

Tenglamani yechish uchun x-12=0 va x+12=0 ni yeching.

$$x=12 x=-12$$

Kvadrat ildizini topish bo'yicha qadamlar

144 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$x^{2}=144$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=12 x=-12$$

Kvadrat tenglamalaridan foydalanish qoidalari

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.

$$x^{2}-144=0$$

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 -144 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-144\right)}}{2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-144\right)}}{2}$$

-4 ni -144 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{576}}{2}$$

576 ning kvadrat ildizini chiqarish.

$$x=\frac{0±24}{2}$$

x=\frac{0±24}{2} tenglamasini yeching, bunda ± musbat. 24 ni 2 ga bo'lish.

$$x=12$$

x=\frac{0±24}{2} tenglamasini yeching, bunda ± manfiy. -24 ni 2 ga bo'lish.

$$x=-12$$

Tenglama yechildi.

$$x=12 x=-12$$