7x^2+4=3x^2-12 eching

$$7 x ^ { 2 } + 4 = 3 x ^ { 2 } - 12$$

x uchun yechish (complex solution)

$$x=-2i$$

$$x=2i$$

Kvadrat ildizini topish bo'yicha qadamlar

Ikkala tarafdan 3x^{2} ni ayirish.

$$7x^{2}+4-3x^{2}=-12$$

4x^{2} ni olish uchun 7x^{2} va -3x^{2} ni birlashtirish.

$$4x^{2}+4=-12$$

Ikkala tarafdan 4 ni ayirish.

$$4x^{2}=-12-4$$

-16 olish uchun -12 dan 4 ni ayirish.

$$4x^{2}=-16$$

Ikki tarafini 4 ga bo‘ling.

$$x^{2}=\frac{-16}{4}$$

-4 ni olish uchun -16 ni 4 ga bo‘ling.

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

Tenglama yechildi.

$$x=2i x=-2i$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 3x^{2} ni ayirish.

$$7x^{2}+4-3x^{2}=-12$$

4x^{2} ni olish uchun 7x^{2} va -3x^{2} ni birlashtirish.

$$4x^{2}+4=-12$$

12 ni ikki tarafga qo’shing.

$$4x^{2}+4+12=0$$

16 olish uchun 4 va 12'ni qo'shing.

$$4x^{2}+16=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 4 ni a, 0 ni b va 16 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\times 16}}{2\times 4}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 4\times 16}}{2\times 4}$$

-4 ni 4 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-16\times 16}}{2\times 4}$$

-16 ni 16 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-256}}{2\times 4}$$

-256 ning kvadrat ildizini chiqarish.

$$x=\frac{0±16i}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{0±16i}{8}$$

x=\frac{0±16i}{8} tenglamasini yeching, bunda ± musbat.

$$x=2i$$

x=\frac{0±16i}{8} tenglamasini yeching, bunda ± manfiy.

$$x=-2i$$

Tenglama yechildi.

$$x=2i x=-2i$$