Solve 6^2=2x^2

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

Solve for x

$$x=3\sqrt{2}\approx 4.242640687$$

$$x=-3\sqrt{2}\approx -4.242640687$$

Steps by Finding Square Root

Calculate 6 to the power of 2 and get 36.

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

Swap sides so that all variable terms are on the left hand side.

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

Divide both sides by 2.

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

Divide 36 by 2 to get 18.

$$x^{2}=18$$

Take the square root of both sides of the equation.

$$x=3\sqrt{2} x=-3\sqrt{2}$$

Steps Using the Quadratic Formula

Calculate 6 to the power of 2 and get 36.

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

Swap sides so that all variable terms are on the left hand side.

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

Subtract 36 from both sides.

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

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

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

Square 0.

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

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-36\right)}}{2\times 2}$$

Multiply -8 times -36.

$$x=\frac{0±\sqrt{288}}{2\times 2}$$

Take the square root of 288.

$$x=\frac{0±12\sqrt{2}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±12\sqrt{2}}{4}$$

Now solve the equation x=\frac{0±12\sqrt{2}}{4} when ± is plus.

$$x=3\sqrt{2}$$

Now solve the equation x=\frac{0±12\sqrt{2}}{4} when ± is minus.

$$x=-3\sqrt{2}$$

The equation is now solved.

$$x=3\sqrt{2} x=-3\sqrt{2}$$