Solve X^2+2x+y^2+4y-20=0

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

Solve for x

$$x=-\frac{X^{2}}{2}-\frac{y^{2}}{2}-2y+10$$

Steps for Solving Linear Equation

Subtract X^{2} from both sides. Anything subtracted from zero gives its negation.

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

Subtract y^{2} from both sides.

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

Subtract 4y from both sides.

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

Add 20 to both sides.

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

The equation is in standard form.

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

Divide both sides by 2.

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

Dividing by 2 undoes the multiplication by 2.

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

Divide -X^{2}-y^{2}-4y+20 by 2.

$$x=-\frac{X^{2}}{2}-\frac{y^{2}}{2}-2y+10$$

Solve for X (complex solution)

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

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

Solve for X

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

$$X=-\sqrt{20-4y-y^{2}-2x}\text{, }x\leq -\frac{y^{2}}{2}-2y+10$$