How to solve (x)^(2)-(1)/(4)=0

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve (x)^(2)-(1)/(4)=0 | Equatix

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Question

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

Solve for x

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

Steps Using Difference of Squares

Steps by Finding Square Root

Steps Using the Quadratic Formula

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.

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

Show Solution

Basic Math

Pre-Algebra

Algebra

Trigonometry

Calculus

Precalculus

Statistics

Finite Math

Linear Algebra

Chemistry

Example

Question

Solve for x

Steps Using Difference of Squares

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps Using Difference of Squares

Steps by Finding Square Root

Steps Using the Quadratic Formula