Solve (x-5)^2=-4(y+2)

$$( x - 5 ) ^ { 2 } = - 4 ( y + 2 )$$

Solve for y

$$y=-\frac{\left(x-5\right)^{2}}{4}-2$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-5\right)^{2}.

$$x^{2}-10x+25=-4\left(y+2\right)$$

Use the distributive property to multiply -4 by y+2.

$$x^{2}-10x+25=-4y-8$$

Swap sides so that all variable terms are on the left hand side.

$$-4y-8=x^{2}-10x+25$$

Add 8 to both sides.

$$-4y=x^{2}-10x+25+8$$

Add 25 and 8 to get 33.

$$-4y=x^{2}-10x+33$$

Divide both sides by -4.

$$\frac{-4y}{-4}=\frac{x^{2}-10x+33}{-4}$$

Dividing by -4 undoes the multiplication by -4.

$$y=\frac{x^{2}-10x+33}{-4}$$

Divide x^{2}-10x+33 by -4.

$$y=-\frac{x^{2}}{4}+\frac{5x}{2}-\frac{33}{4}$$

Solve for x (complex solution)

$$x=-2\sqrt{-y-2}+5$$

$$x=2\sqrt{-y-2}+5$$

Solve for x

$$x=-2\sqrt{-y-2}+5$$

$$x=2\sqrt{-y-2}+5\text{, }y\leq -2$$