2x^2+2y-12x+8=24 eching

$$2 { x }^{ 2 } +2y-12x+8=24$$

y uchun yechish

$$y=8+6x-x^{2}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikkala tarafdan 2x^{2} ni ayirish.

$$2y-12x+8=24-2x^{2}$$

12x ni ikki tarafga qo’shing.

$$2y+8=24-2x^{2}+12x$$

Ikkala tarafdan 8 ni ayirish.

$$2y=24-2x^{2}+12x-8$$

16 olish uchun 24 dan 8 ni ayirish.

$$2y=16-2x^{2}+12x$$

Tenglama standart shaklda.

$$2y=16+12x-2x^{2}$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2y}{2}=\frac{16+12x-2x^{2}}{2}$$

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

$$y=\frac{16+12x-2x^{2}}{2}$$

16-2x^{2}+12x ni 2 ga bo'lish.

$$y=8+6x-x^{2}$$

x uchun yechish (complex solution)

$$x=\sqrt{17-y}+3$$

$$x=-\sqrt{17-y}+3$$

x uchun yechish

$$x=\sqrt{17-y}+3$$

$$x=-\sqrt{17-y}+3\text{, }y\leq 17$$