Solve sqrt{(2x+5)}=sqrt{(x+7)}

$$\sqrt { ( 2 x + 5 ) } = \sqrt { ( x + 7 ) }$$

Solve for x

$$x=2$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{2x+5}\right)^{2}=\left(\sqrt{x+7}\right)^{2}$$

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

$$2x+5=\left(\sqrt{x+7}\right)^{2}$$

Calculate \sqrt{x+7} to the power of 2 and get x+7.

$$2x+5=x+7$$

Subtract x from both sides.

$$2x+5-x=7$$

Combine 2x and -x to get x.

$$x+5=7$$

Subtract 5 from both sides.

$$x=7-5$$

Subtract 5 from 7 to get 2.

$$x=2$$

Substitute 2 for x in the equation \sqrt{2x+5}=\sqrt{x+7}.

$$\sqrt{2\times 2+5}=\sqrt{2+7}$$

Simplify. The value x=2 satisfies the equation.

$$3=3$$

Equation \sqrt{2x+5}=\sqrt{x+7} has a unique solution.

$$x=2$$