Solve sqrt{3x+12}=sqrt{x+8}

$$\sqrt{ 3x+12 } = \sqrt{ x+8 }$$

Solve for x

$$x=-2$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{3x+12}\right)^{2}=\left(\sqrt{x+8}\right)^{2}$$

Calculate \sqrt{3x+12} to the power of 2 and get 3x+12.

$$3x+12=\left(\sqrt{x+8}\right)^{2}$$

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

$$3x+12=x+8$$

Subtract x from both sides.

$$3x+12-x=8$$

Combine 3x and -x to get 2x.

$$2x+12=8$$

Subtract 12 from both sides.

$$2x=8-12$$

Subtract 12 from 8 to get -4.

$$2x=-4$$

Divide both sides by 2.

$$x=\frac{-4}{2}$$

Divide -4 by 2 to get -2.

$$x=-2$$

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

$$\sqrt{3\left(-2\right)+12}=\sqrt{-2+8}$$

Simplify. The value x=-2 satisfies the equation.

$$6^{\frac{1}{2}}=6^{\frac{1}{2}}$$

Equation \sqrt{3x+12}=\sqrt{x+8} has a unique solution.

$$x=-2$$