Solve sqrt{2x+4}=sqrt{3x-8}

$$\sqrt { 2 x + 4 } = \sqrt { 3 x - 8 }$$

Solve for x

$$x=12$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{2x+4}\right)^{2}=\left(\sqrt{3x-8}\right)^{2}$$

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

$$2x+4=\left(\sqrt{3x-8}\right)^{2}$$

Calculate \sqrt{3x-8} to the power of 2 and get 3x-8.

$$2x+4=3x-8$$

Subtract 3x from both sides.

$$2x+4-3x=-8$$

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

$$-x+4=-8$$

Subtract 4 from both sides.

$$-x=-8-4$$

Subtract 4 from -8 to get -12.

$$-x=-12$$

Multiply both sides by -1.

$$x=12$$

Substitute 12 for x in the equation \sqrt{2x+4}=\sqrt{3x-8}.

$$\sqrt{2\times 12+4}=\sqrt{3\times 12-8}$$

Simplify. The value x=12 satisfies the equation.

$$2\times 7^{\frac{1}{2}}=2\times 7^{\frac{1}{2}}$$

Equation \sqrt{2x+4}=\sqrt{3x-8} has a unique solution.

$$x=12$$