+y^2-4x-2y-20=0 eching

$$+ y ^ { 2 } - 4 x - 2 y - 20 = 0$$

x uchun yechish

$$x=\frac{y^{2}-2y-20}{4}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$-4x-2y-20=-y^{2}$$

2y ni ikki tarafga qo’shing.

$$-4x-20=-y^{2}+2y$$

20 ni ikki tarafga qo’shing.

$$-4x=-y^{2}+2y+20$$

Tenglama standart shaklda.

$$-4x=20+2y-y^{2}$$

Ikki tarafini -4 ga bo‘ling.

$$\frac{-4x}{-4}=\frac{20+2y-y^{2}}{-4}$$

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

$$x=\frac{20+2y-y^{2}}{-4}$$

-y^{2}+2y+20 ni -4 ga bo'lish.

$$x=\frac{y^{2}}{4}-\frac{y}{2}-5$$

y uchun yechish (complex solution)

$$y=\sqrt{4x+21}+1$$

$$y=-\sqrt{4x+21}+1$$

y uchun yechish

$$y=\sqrt{4x+21}+1$$

$$y=-\sqrt{4x+21}+1\text{, }x\geq -\frac{21}{4}$$