2(3x-5)^2+32=0 eching

$$2 ( 3 x - 5 ) ^ { 2 } + 32 = 0$$

x uchun yechish (complex solution)

$$x=\frac{5}{3}-\frac{4}{3}i\approx 1,666666667-1,333333333i$$

$$x=\frac{5}{3}+\frac{4}{3}i\approx 1,666666667+1,333333333i$$

Kvadrat ildizini topish bo'yicha qadamlar

O‘zidan 32 ayirilsa 0 qoladi.

$$2\left(3x-5\right)^{2}=-32$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2\left(3x-5\right)^{2}}{2}=-\frac{32}{2}$$

2 ga bo'lish 2 ga ko'paytirishni bekor qiladi.

$$\left(3x-5\right)^{2}=-\frac{32}{2}$$

-32 ni 2 ga bo'lish.

$$\left(3x-5\right)^{2}=-16$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$3x-5=4i 3x-5=-4i$$

5 ni tenglamaning ikkala tarafiga qo'shish.

$$3x-5-\left(-5\right)=4i-\left(-5\right) 3x-5-\left(-5\right)=-4i-\left(-5\right)$$

O‘zidan -5 ayirilsa 0 qoladi.

$$3x=4i-\left(-5\right) 3x=-4i-\left(-5\right)$$

4i dan -5 ni ayirish.

$$3x=5+4i$$

-4i dan -5 ni ayirish.

$$3x=5-4i$$

Ikki tarafini 3 ga bo‘ling.

$$\frac{3x}{3}=\frac{5+4i}{3} \frac{3x}{3}=\frac{5-4i}{3}$$

3 ga bo'lish 3 ga ko'paytirishni bekor qiladi.

$$x=\frac{5+4i}{3} x=\frac{5-4i}{3}$$

5+4i ni 3 ga bo'lish.

$$x=\frac{5}{3}+\frac{4}{3}i$$

5-4i ni 3 ga bo'lish.

$$x=\frac{5}{3}-\frac{4}{3}i$$

Tenglama yechildi.

$$x=\frac{5}{3}+\frac{4}{3}i x=\frac{5}{3}-\frac{4}{3}i$$