x^2=2x^2/4-8 eching

$$x ^ { 2 } = \frac { 2 x ^ { 2 } } { 4 } - 8$$

x uchun yechish (complex solution)

$$x=-4i$$

$$x=4i$$

Kvadrat ildizini topish bo'yicha qadamlar

Tenglamaning ikkala tarafini 4 ga ko'paytirish.

$$4x^{2}=2x^{2}-32$$

Ikkala tarafdan 2x^{2} ni ayirish.

$$4x^{2}-2x^{2}=-32$$

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

$$2x^{2}=-32$$

Ikki tarafini 2 ga bo‘ling.

$$x^{2}=\frac{-32}{2}$$

-16 ni olish uchun -32 ni 2 ga bo‘ling.

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

Tenglama yechildi.

$$x=4i x=-4i$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tenglamaning ikkala tarafini 4 ga ko'paytirish.

$$4x^{2}=2x^{2}-32$$

Ikkala tarafdan 2x^{2} ni ayirish.

$$4x^{2}-2x^{2}=-32$$

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

$$2x^{2}=-32$$

32 ni ikki tarafga qo’shing.

$$2x^{2}+32=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, 0 ni b va 32 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\times 32}}{2\times 2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 2\times 32}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-8\times 32}}{2\times 2}$$

-8 ni 32 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-256}}{2\times 2}$$

-256 ning kvadrat ildizini chiqarish.

$$x=\frac{0±16i}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{0±16i}{4}$$

x=\frac{0±16i}{4} tenglamasini yeching, bunda ± musbat.

$$x=4i$$

x=\frac{0±16i}{4} tenglamasini yeching, bunda ± manfiy.

$$x=-4i$$

Tenglama yechildi.

$$x=4i x=-4i$$