Solve sqrt{2x+16}=2x+4

$$\sqrt{ 2x+16 } =2x+4$$

Solve for x

$$x=0$$

Solution Steps

Square both sides of the equation.

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

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

$$2x+16=\left(2x+4\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+4\right)^{2}.

$$2x+16=4x^{2}+16x+16$$

Subtract 4x^{2} from both sides.

$$2x+16-4x^{2}=16x+16$$

Subtract 16x from both sides.

$$2x+16-4x^{2}-16x=16$$

Combine 2x and -16x to get -14x.

$$-14x+16-4x^{2}=16$$

Subtract 16 from both sides.

$$-14x+16-4x^{2}-16=0$$

Subtract 16 from 16 to get 0.

$$-14x-4x^{2}=0$$

Factor out x.

$$x\left(-14-4x\right)=0$$

To find equation solutions, solve x=0 and -14-4x=0.

$$x=0 x=-\frac{7}{2}$$

Substitute 0 for x in the equation \sqrt{2x+16}=2x+4.

$$\sqrt{2\times 0+16}=2\times 0+4$$

Simplify. The value x=0 satisfies the equation.

$$4=4$$

Substitute -\frac{7}{2} for x in the equation \sqrt{2x+16}=2x+4.

$$\sqrt{2\left(-\frac{7}{2}\right)+16}=2\left(-\frac{7}{2}\right)+4$$

Simplify. The value x=-\frac{7}{2} does not satisfy the equation because the left and the right hand side have opposite signs.

$$3=-3$$

Equation \sqrt{2x+16}=2x+4 has a unique solution.

$$x=0$$