x^2+6x-y+9=0 eching

$$x ^ { 2 } + 6 x - y + 9 = 0$$

y uchun yechish

$$y=\left(x+3\right)^{2}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikkala tarafdan x^{2} ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$6x-y+9=-x^{2}$$

Ikkala tarafdan 6x ni ayirish.

$$-y+9=-x^{2}-6x$$

Ikkala tarafdan 9 ni ayirish.

$$-y=-x^{2}-6x-9$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-y}{-1}=-\frac{\left(x+3\right)^{2}}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$y=-\frac{\left(x+3\right)^{2}}{-1}$$

-\left(x+3\right)^{2} ni -1 ga bo'lish.

$$y=\left(x+3\right)^{2}$$

x uchun yechish (complex solution)

$$x=\sqrt{y}-3$$

$$x=-\sqrt{y}-3$$

x uchun yechish

$$x=\sqrt{y}-3$$

$$x=-\sqrt{y}-3\text{, }y\geq 0$$