1/4(x+1)^2+16=0 eching

$$\frac { 1 } { 4 } ( x + 1 ) ^ { 2 } + 16 = 0$$

x uchun yechish (complex solution)

$$x=-1-8i$$

$$x=-1+8i$$

Kvadrat ildizini topish bo'yicha qadamlar

O‘zidan 16 ayirilsa 0 qoladi.

$$\frac{1}{4}\left(x+1\right)^{2}=-16$$

Ikkala tarafini 4 ga ko‘paytiring.

$$\frac{\frac{1}{4}\left(x+1\right)^{2}}{\frac{1}{4}}=-\frac{16}{\frac{1}{4}}$$

\frac{1}{4} ga bo'lish \frac{1}{4} ga ko'paytirishni bekor qiladi.

$$\left(x+1\right)^{2}=-\frac{16}{\frac{1}{4}}$$

-16 ni \frac{1}{4} ga bo'lish -16 ga k'paytirish \frac{1}{4} ga qaytarish.

$$\left(x+1\right)^{2}=-64$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x+1=8i x+1=-8i$$

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$x+1-1=8i-1 x+1-1=-8i-1$$

O‘zidan 1 ayirilsa 0 qoladi.

$$x=8i-1 x=-8i-1$$

8i dan 1 ni ayirish.

$$x=-1+8i$$

-8i dan 1 ni ayirish.

$$x=-1-8i$$

Tenglama yechildi.

$$x=-1+8i x=-1-8i$$