Solve x^2+(2sqrt{3})^2=(2x)^2

$$x ^ { 2 } + ( 2 \sqrt { 3 } ) ^ { 2 } = ( 2 x ) ^ { 2 }$$

Solve for x

$$x=2$$

$$x=-2$$

Steps by Finding Square Root

Expand \left(2\sqrt{3}\right)^{2}.

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

Calculate 2 to the power of 2 and get 4.

$$x^{2}+4\left(\sqrt{3}\right)^{2}=\left(2x\right)^{2}$$

The square of \sqrt{3} is 3.

$$x^{2}+4\times 3=\left(2x\right)^{2}$$

Multiply 4 and 3 to get 12.

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

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

$$x^{2}+12=2^{2}x^{2}$$

Calculate 2 to the power of 2 and get 4.

$$x^{2}+12=4x^{2}$$

Subtract 4x^{2} from both sides.

$$x^{2}+12-4x^{2}=0$$

Combine x^{2} and -4x^{2} to get -3x^{2}.

$$-3x^{2}+12=0$$

Subtract 12 from both sides. Anything subtracted from zero gives its negation.

$$-3x^{2}=-12$$

Divide both sides by -3.

$$x^{2}=\frac{-12}{-3}$$

Divide -12 by -3 to get 4.

$$x^{2}=4$$

Take the square root of both sides of the equation.

$$x=2 x=-2$$

Steps Using the Quadratic Formula

Expand \left(2\sqrt{3}\right)^{2}.

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

Calculate 2 to the power of 2 and get 4.

$$x^{2}+4\left(\sqrt{3}\right)^{2}=\left(2x\right)^{2}$$

The square of \sqrt{3} is 3.

$$x^{2}+4\times 3=\left(2x\right)^{2}$$

Multiply 4 and 3 to get 12.

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

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

$$x^{2}+12=2^{2}x^{2}$$

Calculate 2 to the power of 2 and get 4.

$$x^{2}+12=4x^{2}$$

Subtract 4x^{2} from both sides.

$$x^{2}+12-4x^{2}=0$$

Combine x^{2} and -4x^{2} to get -3x^{2}.

$$-3x^{2}+12=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -3 for a, 0 for b, and 12 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-3\right)\times 12}}{2\left(-3\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-3\right)\times 12}}{2\left(-3\right)}$$

Multiply -4 times -3.

$$x=\frac{0±\sqrt{12\times 12}}{2\left(-3\right)}$$

Multiply 12 times 12.

$$x=\frac{0±\sqrt{144}}{2\left(-3\right)}$$

Take the square root of 144.

$$x=\frac{0±12}{2\left(-3\right)}$$

Multiply 2 times -3.

$$x=\frac{0±12}{-6}$$

Now solve the equation x=\frac{0±12}{-6} when ± is plus. Divide 12 by -6.

$$x=-2$$

Now solve the equation x=\frac{0±12}{-6} when ± is minus. Divide -12 by -6.

$$x=2$$

The equation is now solved.

$$x=-2 x=2$$