Solve x^2-1/4=0

$${ x }^{ 2 } - \frac{ 1 }{ 4 } =0$$

Solve for x

$$x=\frac{1}{2}=0.5$$

$$x=-\frac{1}{2}=-0.5$$

Steps Using Difference of Squares

Multiply both sides by 4.

$$4x^{2}-1=0$$

Consider 4x^{2}-1. Rewrite 4x^{2}-1 as \left(2x\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).

$$\left(2x-1\right)\left(2x+1\right)=0$$

To find equation solutions, solve 2x-1=0 and 2x+1=0.

$$x=\frac{1}{2} x=-\frac{1}{2}$$

Steps by Finding Square Root

Add \frac{1}{4} to both sides. Anything plus zero gives itself.

$$x^{2}=\frac{1}{4}$$

Take the square root of both sides of the equation.

$$x=\frac{1}{2} x=-\frac{1}{2}$$

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.

$$x^{2}-\frac{1}{4}=0$$

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

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

Square 0.

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

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

$$x=\frac{0±\sqrt{1}}{2}$$

Take the square root of 1.

$$x=\frac{0±1}{2}$$

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

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

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

$$x=-\frac{1}{2}$$

The equation is now solved.

$$x=\frac{1}{2} x=-\frac{1}{2}$$