3x^2+4=436 eching

$$3 x ^ { 2 } + 4 = 436$$

x uchun yechish

$$x=12$$

$$x=-12$$

Kvadratlar farqidan foydalangan qadamlar

Ikkala tarafdan 436 ni ayirish.

$$3x^{2}+4-436=0$$

-432 olish uchun 4 dan 436 ni ayirish.

$$3x^{2}-432=0$$

Ikki tarafini 3 ga bo‘ling.

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

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

Ikkala tarafdan 4 ni ayirish.

$$3x^{2}=436-4$$

432 olish uchun 436 dan 4 ni ayirish.

$$3x^{2}=432$$

Ikki tarafini 3 ga bo‘ling.

$$x^{2}=\frac{432}{3}$$

144 ni olish uchun 432 ni 3 ga bo‘ling.

$$x^{2}=144$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=12 x=-12$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 436 ni ayirish.

$$3x^{2}+4-436=0$$

-432 olish uchun 4 dan 436 ni ayirish.

$$3x^{2}-432=0$$

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 -432 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-432\right)}}{2\times 3}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 3\left(-432\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-12\left(-432\right)}}{2\times 3}$$

-12 ni -432 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{5184}}{2\times 3}$$

5184 ning kvadrat ildizini chiqarish.

$$x=\frac{0±72}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{0±72}{6}$$

x=\frac{0±72}{6} tenglamasini yeching, bunda ± musbat. 72 ni 6 ga bo'lish.

$$x=12$$

x=\frac{0±72}{6} tenglamasini yeching, bunda ± manfiy. -72 ni 6 ga bo'lish.

$$x=-12$$

Tenglama yechildi.

$$x=12 x=-12$$