How do you solve the equation 2x^2-512=0?

Apr 28, 2017

$x = \pm 16$

Explanation:

Add $512$ to both sides:

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

This becomes:

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

Divide both sides by $2$:

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

This becomes:

${x}^{2} = 256$

Square root both sides:

$\sqrt{{x}^{2}} = \pm \sqrt{256}$

This becomes:

$x = \pm \sqrt{256}$

Break down $256$ into its factors:

$x = \pm \sqrt{2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2}$

Take out pairs of the same number:

$x = \pm \left(2 \cdot 2 \cdot 2 \cdot 2\right)$

This leaves you with:

$x = \pm 16$