Solve sqrt{5+x/2-z}=5

$$\sqrt { \frac { 5 + x } { 2 } - z } = 5$$

Solve for x

$$x=2z+45$$

Steps for Solving Radical Equations

Divide each term of 5+x by 2 to get \frac{5}{2}+\frac{1}{2}x.

$$\sqrt{\frac{5}{2}+\frac{1}{2}x-z}=5$$

Square both sides of the equation.

$$\frac{1}{2}x+\frac{5}{2}-z=25$$

Subtract \frac{5}{2}-z from both sides of the equation.

$$\frac{1}{2}x+\frac{5}{2}-z-\left(\frac{5}{2}-z\right)=25-\left(\frac{5}{2}-z\right)$$

Subtracting \frac{5}{2}-z from itself leaves 0.

$$\frac{1}{2}x=25-\left(\frac{5}{2}-z\right)$$

Subtract \frac{5}{2}-z from 25.

$$\frac{1}{2}x=z+\frac{45}{2}$$

Multiply both sides by 2.

$$\frac{\frac{1}{2}x}{\frac{1}{2}}=\frac{z+\frac{45}{2}}{\frac{1}{2}}$$

Dividing by \frac{1}{2} undoes the multiplication by \frac{1}{2}.

$$x=\frac{z+\frac{45}{2}}{\frac{1}{2}}$$

Divide \frac{45}{2}+z by \frac{1}{2} by multiplying \frac{45}{2}+z by the reciprocal of \frac{1}{2}.

$$x=2z+45$$

Solve for z

$$z=\frac{x-45}{2}$$

Steps for Solving Radical Equations

Square both sides of the equation.

$$-z+\frac{x+5}{2}=25$$

Subtract \frac{5}{2}+\frac{1}{2}x from both sides of the equation.

$$-z+\frac{x+5}{2}-\frac{x+5}{2}=25-\frac{x+5}{2}$$

Subtracting \frac{5}{2}+\frac{1}{2}x from itself leaves 0.

$$-z=25-\frac{x+5}{2}$$

Subtract \frac{5}{2}+\frac{1}{2}x from 25.

$$-z=\frac{45-x}{2}$$

Divide both sides by -1.

$$\frac{-z}{-1}=\frac{45-x}{-2}$$

Dividing by -1 undoes the multiplication by -1.

$$z=\frac{45-x}{-2}$$

Divide \frac{45-x}{2} by -1.

$$z=\frac{x-45}{2}$$