Solve sqrt{x+15}=sqrt{3x+1}

$$\sqrt{ x+15 } = \sqrt{ 3x+1 }$$

Solve for x

$$x=7$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{x+15}\right)^{2}=\left(\sqrt{3x+1}\right)^{2}$$

Calculate \sqrt{x+15} to the power of 2 and get x+15.

$$x+15=\left(\sqrt{3x+1}\right)^{2}$$

Calculate \sqrt{3x+1} to the power of 2 and get 3x+1.

$$x+15=3x+1$$

Subtract 3x from both sides.

$$x+15-3x=1$$

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

$$-2x+15=1$$

Subtract 15 from both sides.

$$-2x=1-15$$

Subtract 15 from 1 to get -14.

$$-2x=-14$$

Divide both sides by -2.

$$x=\frac{-14}{-2}$$

Divide -14 by -2 to get 7.

$$x=7$$

Substitute 7 for x in the equation \sqrt{x+15}=\sqrt{3x+1}.

$$\sqrt{7+15}=\sqrt{3\times 7+1}$$

Simplify. The value x=7 satisfies the equation.

$$22^{\frac{1}{2}}=22^{\frac{1}{2}}$$

Equation \sqrt{x+15}=\sqrt{3x+1} has a unique solution.

$$x=7$$