Solve x*2x=512

$$x \times 2x=512$$

Solve for x

$$x=16$$

$$x=-16$$

Steps by Finding Square Root

Multiply x and x to get x^{2}.

$$x^{2}\times 2=512$$

Divide both sides by 2.

$$x^{2}=\frac{512}{2}$$

Divide 512 by 2 to get 256.

$$x^{2}=256$$

Take the square root of both sides of the equation.

$$x=16 x=-16$$

Steps Using the Quadratic Formula

Multiply x and x to get x^{2}.

$$x^{2}\times 2=512$$

Subtract 512 from both sides.

$$x^{2}\times 2-512=0$$

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.

$$2x^{2}-512=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -512 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-512\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-512\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-512\right)}}{2\times 2}$$

Multiply -8 times -512.

$$x=\frac{0±\sqrt{4096}}{2\times 2}$$

Take the square root of 4096.

$$x=\frac{0±64}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±64}{4}$$

Now solve the equation x=\frac{0±64}{4} when ± is plus. Divide 64 by 4.

$$x=16$$

Now solve the equation x=\frac{0±64}{4} when ± is minus. Divide -64 by 4.

$$x=-16$$

The equation is now solved.

$$x=16 x=-16$$