Solve (6-2sqrt{x})^2+8x=6^2

$$( 6 - 2 \sqrt { x } ) ^ { 2 } + 8 x = 6 ^ { 2 }$$

Solve for x

$$x=0$$

$$x=4$$

Solution Steps

Calculate 6 to the power of 2 and get 36.

$$\left(6-2\sqrt{x}\right)^{2}+8x=36$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(6-2\sqrt{x}\right)^{2}.

$$36-24\sqrt{x}+4\left(\sqrt{x}\right)^{2}+8x=36$$

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

$$36-24\sqrt{x}+4x+8x=36$$

Combine 4x and 8x to get 12x.

$$36-24\sqrt{x}+12x=36$$

Subtract 36 from both sides.

$$-24\sqrt{x}+12x=36-36$$

Subtract 36 from 36 to get 0.

$$-24\sqrt{x}+12x=0$$

Subtract 12x from both sides of the equation.

$$-24\sqrt{x}=-12x$$

Square both sides of the equation.

$$\left(-24\sqrt{x}\right)^{2}=\left(-12x\right)^{2}$$

Expand \left(-24\sqrt{x}\right)^{2}.

$$\left(-24\right)^{2}\left(\sqrt{x}\right)^{2}=\left(-12x\right)^{2}$$

Calculate -24 to the power of 2 and get 576.

$$576\left(\sqrt{x}\right)^{2}=\left(-12x\right)^{2}$$

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

$$576x=\left(-12x\right)^{2}$$

Expand \left(-12x\right)^{2}.

$$576x=\left(-12\right)^{2}x^{2}$$

Calculate -12 to the power of 2 and get 144.

$$576x=144x^{2}$$

Subtract 144x^{2} from both sides.

$$576x-144x^{2}=0$$

Factor out x.

$$x\left(576-144x\right)=0$$

To find equation solutions, solve x=0 and 576-144x=0.

$$x=0 x=4$$

Substitute 0 for x in the equation \left(6-2\sqrt{x}\right)^{2}+8x=6^{2}.

$$\left(6-2\sqrt{0}\right)^{2}+8\times 0=6^{2}$$

Simplify. The value x=0 satisfies the equation.

$$36=36$$

Substitute 4 for x in the equation \left(6-2\sqrt{x}\right)^{2}+8x=6^{2}.

$$\left(6-2\sqrt{4}\right)^{2}+8\times 4=6^{2}$$

Simplify. The value x=4 satisfies the equation.

$$36=36$$

List all solutions of -24\sqrt{x}=-12x.

$$x=0 x=4$$