Solve sqrt{225-y}-y=15

$$\sqrt { 225 - y } - y = 15$$

Solve for y

$$y=0$$

Solution Steps

Subtract -y from both sides of the equation.

$$\sqrt{225-y}=15+y$$

Square both sides of the equation.

$$\left(\sqrt{225-y}\right)^{2}=\left(15+y\right)^{2}$$

Calculate \sqrt{225-y} to the power of 2 and get 225-y.

$$225-y=\left(15+y\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(15+y\right)^{2}.

$$225-y=225+30y+y^{2}$$

Subtract 225 from both sides.

$$225-y-225=30y+y^{2}$$

Subtract 225 from 225 to get 0.

$$-y=30y+y^{2}$$

Subtract 30y from both sides.

$$-y-30y=y^{2}$$

Combine -y and -30y to get -31y.

$$-31y=y^{2}$$

Subtract y^{2} from both sides.

$$-31y-y^{2}=0$$

Factor out y.

$$y\left(-31-y\right)=0$$

To find equation solutions, solve y=0 and -31-y=0.

$$y=0 y=-31$$

Substitute 0 for y in the equation \sqrt{225-y}-y=15.

$$\sqrt{225-0}-0=15$$

Simplify. The value y=0 satisfies the equation.

$$15=15$$

Substitute -31 for y in the equation \sqrt{225-y}-y=15.

$$\sqrt{225-\left(-31\right)}-\left(-31\right)=15$$

Simplify. The value y=-31 does not satisfy the equation.

$$47=15$$

Equation \sqrt{225-y}=y+15 has a unique solution.

$$y=0$$