Solve sqrt{5x+1}=x+1

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

Solve for x

$$x=3$$

$$x=0$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{5x+1}\right)^{2}=\left(x+1\right)^{2}$$

Calculate \sqrt{5x+1} to the power of 2 and get 5x+1.

$$5x+1=\left(x+1\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.

$$5x+1=x^{2}+2x+1$$

Subtract x^{2} from both sides.

$$5x+1-x^{2}=2x+1$$

Subtract 2x from both sides.

$$5x+1-x^{2}-2x=1$$

Combine 5x and -2x to get 3x.

$$3x+1-x^{2}=1$$

Subtract 1 from both sides.

$$3x+1-x^{2}-1=0$$

Subtract 1 from 1 to get 0.

$$3x-x^{2}=0$$

Factor out x.

$$x\left(3-x\right)=0$$

To find equation solutions, solve x=0 and 3-x=0.

$$x=0 x=3$$

Substitute 0 for x in the equation \sqrt{5x+1}=x+1.

$$\sqrt{5\times 0+1}=0+1$$

Simplify. The value x=0 satisfies the equation.

$$1=1$$

Substitute 3 for x in the equation \sqrt{5x+1}=x+1.

$$\sqrt{5\times 3+1}=3+1$$

Simplify. The value x=3 satisfies the equation.

$$4=4$$

List all solutions of \sqrt{5x+1}=x+1.

$$x=0 x=3$$