x^2+6x-4y+1=0 eching

$$x ^ { 2 } + 6 x - 4 y + 1 = 0$$

y uchun yechish

$$y=\frac{x^{2}+6x+1}{4}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$6x-4y+1=-x^{2}$$

Ikkala tarafdan 6x ni ayirish.

$$-4y+1=-x^{2}-6x$$

Ikkala tarafdan 1 ni ayirish.

$$-4y=-x^{2}-6x-1$$

Ikki tarafini -4 ga bo‘ling.

$$\frac{-4y}{-4}=\frac{-x^{2}-6x-1}{-4}$$

-4 ga bo'lish -4 ga ko'paytirishni bekor qiladi.

$$y=\frac{-x^{2}-6x-1}{-4}$$

-x^{2}-6x-1 ni -4 ga bo'lish.

$$y=\frac{x^{2}}{4}+\frac{3x}{2}+\frac{1}{4}$$

x uchun yechish (complex solution)

$$x=2\sqrt{y+2}-3$$

$$x=-2\sqrt{y+2}-3$$

x uchun yechish

$$x=2\sqrt{y+2}-3$$

$$x=-2\sqrt{y+2}-3\text{, }y\geq -2$$