Solve sqrt{x}+5=x+5

$$\sqrt { x } + 5 = x + 5$$

Solve for x

$$x=0$$

$$x=1$$

Solution Steps

Subtract 5 from both sides of the equation.

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

Subtract 5 from 5 to get 0.

$$\sqrt{x}=x$$

Square both sides of the equation.

$$\left(\sqrt{x}\right)^{2}=x^{2}$$

Calculate \sqrt{x} to the power of 2 and get x.

$$x=x^{2}$$

Subtract x^{2} from both sides.

$$x-x^{2}=0$$

Factor out x.

$$x\left(1-x\right)=0$$

To find equation solutions, solve x=0 and 1-x=0.

$$x=0 x=1$$

Substitute 0 for x in the equation \sqrt{x}+5=x+5.

$$\sqrt{0}+5=0+5$$

Simplify. The value x=0 satisfies the equation.

$$5=5$$

Substitute 1 for x in the equation \sqrt{x}+5=x+5.

$$\sqrt{1}+5=1+5$$

Simplify. The value x=1 satisfies the equation.

$$6=6$$

List all solutions of \sqrt{x}=x.

$$x=0 x=1$$