Solve left(x+5right)^2=-20(y-9.5)

$${ \left(x+5 \right) }^{ 2 } =-20(y-9.5)$$

Solve for y

$$y=-\frac{\left(x+5\right)^{2}}{20}+9.5$$

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}.

$$x^{2}+10x+25=-20\left(y-9.5\right)$$

Use the distributive property to multiply -20 by y-9.5.

$$x^{2}+10x+25=-20y+190$$

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

$$-20y+190=x^{2}+10x+25$$

Subtract 190 from both sides.

$$-20y=x^{2}+10x+25-190$$

Subtract 190 from 25 to get -165.

$$-20y=x^{2}+10x-165$$

Divide both sides by -20.

$$\frac{-20y}{-20}=\frac{x^{2}+10x-165}{-20}$$

Dividing by -20 undoes the multiplication by -20.

$$y=\frac{x^{2}+10x-165}{-20}$$

Divide x^{2}+10x-165 by -20.

$$y=-\frac{x^{2}}{20}-\frac{x}{2}+\frac{33}{4}$$

Solve for x (complex solution)

$$x=-\sqrt{190-20y}-5$$

$$x=\sqrt{190-20y}-5$$

Solve for x

$$x=-\sqrt{190-20y}-5$$

$$x=\sqrt{190-20y}-5\text{, }y\leq \frac{19}{2}$$