Solve x^2=256

$$x ^ { 2 } = 256$$

Solve for x

$$x=16$$

$$x=-16$$

Steps Using Difference of Squares

Subtract 256 from both sides.

$$x^{2}-256=0$$

Consider x^{2}-256. Rewrite x^{2}-256 as x^{2}-16^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-16\right)\left(x+16\right)=0$$

To find equation solutions, solve x-16=0 and x+16=0.

$$x=16 x=-16$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x=16 x=-16$$

Steps Using the Quadratic Formula

Subtract 256 from both sides.

$$x^{2}-256=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -256 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-256\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-256\right)}}{2}$$

Multiply -4 times -256.

$$x=\frac{0±\sqrt{1024}}{2}$$

Take the square root of 1024.

$$x=\frac{0±32}{2}$$

Now solve the equation x=\frac{0±32}{2} when ± is plus. Divide 32 by 2.

$$x=16$$

Now solve the equation x=\frac{0±32}{2} when ± is minus. Divide -32 by 2.

$$x=-16$$

The equation is now solved.

$$x=16 x=-16$$