Solve x^2-1/64=0

$$x ^ { 2 } - \frac { 1 } { 64 } = 0$$

Solve for x

$$x=\frac{1}{8}=0.125$$

$$x=-\frac{1}{8}=-0.125$$

Steps Using Difference of Squares

Multiply both sides by 64.

$$64x^{2}-1=0$$

Consider 64x^{2}-1. Rewrite 64x^{2}-1 as \left(8x\right)^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(8x-1\right)\left(8x+1\right)=0$$

To find equation solutions, solve 8x-1=0 and 8x+1=0.

$$x=\frac{1}{8} x=-\frac{1}{8}$$

Steps by Finding Square Root

Add \frac{1}{64} to both sides. Anything plus zero gives itself.

$$x^{2}=\frac{1}{64}$$

Take the square root of both sides of the equation.

$$x=\frac{1}{8} x=-\frac{1}{8}$$

Steps Using the Quadratic Formula

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.

$$x^{2}-\frac{1}{64}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{1}{64} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{1}{64}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{1}{64}\right)}}{2}$$

Multiply -4 times -\frac{1}{64}.

$$x=\frac{0±\sqrt{\frac{1}{16}}}{2}$$

Take the square root of \frac{1}{16}.

$$x=\frac{0±\frac{1}{4}}{2}$$

Now solve the equation x=\frac{0±\frac{1}{4}}{2} when ± is plus.

$$x=\frac{1}{8}$$

Now solve the equation x=\frac{0±\frac{1}{4}}{2} when ± is minus.

$$x=-\frac{1}{8}$$

The equation is now solved.

$$x=\frac{1}{8} x=-\frac{1}{8}$$