Solve 12^2+x^2=left(2xright)^2

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

Solve for x

$$x=4\sqrt{3}\approx 6.92820323$$

$$x=-4\sqrt{3}\approx -6.92820323$$

Steps by Finding Square Root

Calculate 12 to the power of 2 and get 144.

$$144+x^{2}=\left(2x\right)^{2}$$

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

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

Calculate 2 to the power of 2 and get 4.

$$144+x^{2}=4x^{2}$$

Subtract 4x^{2} from both sides.

$$144+x^{2}-4x^{2}=0$$

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

$$144-3x^{2}=0$$

Subtract 144 from both sides. Anything subtracted from zero gives its negation.

$$-3x^{2}=-144$$

Divide both sides by -3.

$$x^{2}=\frac{-144}{-3}$$

Divide -144 by -3 to get 48.

$$x^{2}=48$$

Take the square root of both sides of the equation.

$$x=4\sqrt{3} x=-4\sqrt{3}$$

Steps Using the Quadratic Formula

Calculate 12 to the power of 2 and get 144.

$$144+x^{2}=\left(2x\right)^{2}$$

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

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

Calculate 2 to the power of 2 and get 4.

$$144+x^{2}=4x^{2}$$

Subtract 4x^{2} from both sides.

$$144+x^{2}-4x^{2}=0$$

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

$$144-3x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-3x^{2}+144=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -3 for a, 0 for b, and 144 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-3\right)\times 144}}{2\left(-3\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-3\right)\times 144}}{2\left(-3\right)}$$

Multiply -4 times -3.

$$x=\frac{0±\sqrt{12\times 144}}{2\left(-3\right)}$$

Multiply 12 times 144.

$$x=\frac{0±\sqrt{1728}}{2\left(-3\right)}$$

Take the square root of 1728.

$$x=\frac{0±24\sqrt{3}}{2\left(-3\right)}$$

Multiply 2 times -3.

$$x=\frac{0±24\sqrt{3}}{-6}$$

Now solve the equation x=\frac{0±24\sqrt{3}}{-6} when ± is plus.

$$x=-4\sqrt{3}$$

Now solve the equation x=\frac{0±24\sqrt{3}}{-6} when ± is minus.

$$x=4\sqrt{3}$$

The equation is now solved.

$$x=-4\sqrt{3} x=4\sqrt{3}$$