Solve x^2+xy+5=0

$${ x }^{ 2 } +xy+5=0$$

Solve for y

$$y=-x-\frac{5}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$xy+5=-x^{2}$$

Subtract 5 from both sides.

$$xy=-x^{2}-5$$

Divide both sides by x.

$$\frac{xy}{x}=\frac{-x^{2}-5}{x}$$

Dividing by x undoes the multiplication by x.

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

Divide -x^{2}-5 by x.

$$y=-x-\frac{5}{x}$$

Solve for x (complex solution)

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

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

Solve for x

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

$$x=\frac{-\sqrt{y^{2}-20}-y}{2}\text{, }|y|\geq 2\sqrt{5}$$