Solve sqrt{4x-8}=sqrt{x+7}

$$\sqrt { 4 x - 8 } = \sqrt { x + 7 }$$

Solve for x

$$x=5$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{4x-8}\right)^{2}=\left(\sqrt{x+7}\right)^{2}$$

Calculate \sqrt{4x-8} to the power of 2 and get 4x-8.

$$4x-8=\left(\sqrt{x+7}\right)^{2}$$

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

$$4x-8=x+7$$

Subtract x from both sides.

$$4x-8-x=7$$

Combine 4x and -x to get 3x.

$$3x-8=7$$

Add 8 to both sides.

$$3x=7+8$$

Add 7 and 8 to get 15.

$$3x=15$$

Divide both sides by 3.

$$x=\frac{15}{3}$$

Divide 15 by 3 to get 5.

$$x=5$$

Substitute 5 for x in the equation \sqrt{4x-8}=\sqrt{x+7}.

$$\sqrt{4\times 5-8}=\sqrt{5+7}$$

Simplify. The value x=5 satisfies the equation.

$$2\times 3^{\frac{1}{2}}=2\times 3^{\frac{1}{2}}$$

Equation \sqrt{4x-8}=\sqrt{x+7} has a unique solution.

$$x=5$$