Solve x^2/2+12^2=x^2

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

Solve for x

$$x=12\sqrt{2}\approx 16.970562748$$

$$x=-12\sqrt{2}\approx -16.970562748$$

Steps by Finding Square Root

Multiply both sides of the equation by 2.

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

Calculate 12 to the power of 2 and get 144.

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

Multiply 2 and 144 to get 288.

$$x^{2}+288=2x^{2}$$

Subtract 2x^{2} from both sides.

$$x^{2}+288-2x^{2}=0$$

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

$$-x^{2}+288=0$$

Subtract 288 from both sides. Anything subtracted from zero gives its negation.

$$-x^{2}=-288$$

Divide both sides by -1.

$$x^{2}=\frac{-288}{-1}$$

Fraction \frac{-288}{-1} can be simplified to 288 by removing the negative sign from both the numerator and the denominator.

$$x^{2}=288$$

Take the square root of both sides of the equation.

$$x=12\sqrt{2} x=-12\sqrt{2}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 2.

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

Calculate 12 to the power of 2 and get 144.

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

Multiply 2 and 144 to get 288.

$$x^{2}+288=2x^{2}$$

Subtract 2x^{2} from both sides.

$$x^{2}+288-2x^{2}=0$$

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

$$-x^{2}+288=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 288 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 288}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 288}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\times 288}}{2\left(-1\right)}$$

Multiply 4 times 288.

$$x=\frac{0±\sqrt{1152}}{2\left(-1\right)}$$

Take the square root of 1152.

$$x=\frac{0±24\sqrt{2}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±24\sqrt{2}}{-2}$$

Now solve the equation x=\frac{0±24\sqrt{2}}{-2} when ± is plus.

$$x=-12\sqrt{2}$$

Now solve the equation x=\frac{0±24\sqrt{2}}{-2} when ± is minus.

$$x=12\sqrt{2}$$

The equation is now solved.

$$x=-12\sqrt{2} x=12\sqrt{2}$$