Solve sqrt{16-2x}=2sqrt{x-8}

$$\sqrt { 16 - 2 x } = 2 \sqrt { x - 8 }$$

Solve for x

$$x=8$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{16-2x}\right)^{2}=\left(2\sqrt{x-8}\right)^{2}$$

Calculate \sqrt{16-2x} to the power of 2 and get 16-2x.

$$16-2x=\left(2\sqrt{x-8}\right)^{2}$$

Expand \left(2\sqrt{x-8}\right)^{2}.

$$16-2x=2^{2}\left(\sqrt{x-8}\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$16-2x=4\left(\sqrt{x-8}\right)^{2}$$

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

$$16-2x=4\left(x-8\right)$$

Use the distributive property to multiply 4 by x-8.

$$16-2x=4x-32$$

Subtract 4x from both sides.

$$16-2x-4x=-32$$

Combine -2x and -4x to get -6x.

$$16-6x=-32$$

Subtract 16 from both sides.

$$-6x=-32-16$$

Subtract 16 from -32 to get -48.

$$-6x=-48$$

Divide both sides by -6.

$$x=\frac{-48}{-6}$$

Divide -48 by -6 to get 8.

$$x=8$$

Substitute 8 for x in the equation \sqrt{16-2x}=2\sqrt{x-8}.

$$\sqrt{16-2\times 8}=2\sqrt{8-8}$$

Simplify. The value x=8 satisfies the equation.

$$0=0$$

Equation \sqrt{16-2x}=2\sqrt{x-8} has a unique solution.

$$x=8$$