Solve x^2+6^2=2x^2

$$x ^ { 2 } + 6 ^ { 2 } = 2 x ^ { 2 }$$

Solve for x

$$x=6$$

$$x=-6$$

Steps by Finding Square Root

Calculate 6 to the power of 2 and get 36.

$$x^{2}+36=2x^{2}$$

Subtract 2x^{2} from both sides.

$$x^{2}+36-2x^{2}=0$$

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

$$-x^{2}+36=0$$

Subtract 36 from both sides. Anything subtracted from zero gives its negation.

$$-x^{2}=-36$$

Divide both sides by -1.

$$x^{2}=\frac{-36}{-1}$$

Fraction \frac{-36}{-1} can be simplified to 36 by removing the negative sign from both the numerator and the denominator.

$$x^{2}=36$$

Take the square root of both sides of the equation.

$$x=6 x=-6$$

Steps Using the Quadratic Formula

Calculate 6 to the power of 2 and get 36.

$$x^{2}+36=2x^{2}$$

Subtract 2x^{2} from both sides.

$$x^{2}+36-2x^{2}=0$$

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

$$-x^{2}+36=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 36 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 36}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 36}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\times 36}}{2\left(-1\right)}$$

Multiply 4 times 36.

$$x=\frac{0±\sqrt{144}}{2\left(-1\right)}$$

Take the square root of 144.

$$x=\frac{0±12}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±12}{-2}$$

Now solve the equation x=\frac{0±12}{-2} when ± is plus. Divide 12 by -2.

$$x=-6$$

Now solve the equation x=\frac{0±12}{-2} when ± is minus. Divide -12 by -2.

$$x=6$$

The equation is now solved.

$$x=-6 x=6$$