Solve sqrt{2x+6}=sqrt{x-7}

$$\sqrt{ 2x+6 } = \sqrt{ x-7 }$$

Solve for x (complex solution)

$$x=-13$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{2x+6}\right)^{2}=\left(\sqrt{x-7}\right)^{2}$$

Calculate \sqrt{2x+6} to the power of 2 and get 2x+6.

$$2x+6=\left(\sqrt{x-7}\right)^{2}$$

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

$$2x+6=x-7$$

Subtract x from both sides.

$$2x+6-x=-7$$

Combine 2x and -x to get x.

$$x+6=-7$$

Subtract 6 from both sides.

$$x=-7-6$$

Subtract 6 from -7 to get -13.

$$x=-13$$

Substitute -13 for x in the equation \sqrt{2x+6}=\sqrt{x-7}.

$$\sqrt{2\left(-13\right)+6}=\sqrt{-13-7}$$

Simplify. The value x=-13 satisfies the equation.

$$2i\times 5^{\frac{1}{2}}=2i\times 5^{\frac{1}{2}}$$

Equation \sqrt{2x+6}=\sqrt{x-7} has a unique solution.

$$x=-13$$