Solve Using the Quadratic Formula 1/4x^2-1=0

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

Step 1

Simplify the left side.

Combine $\frac{1}{4}$ and $x^{2}$ .

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

Step 2

Multiply through by the least common denominator $4$ , then simplify.

Apply the distributive property.

$4 (\frac{x^{2}}{4}) + 4 \cdot - 1 = 0$

Cancel the common factor of $4$ .

Cancel the common factor.

$4 (\frac{x^{2}}{4}) + 4 \cdot - 1 = 0$

Rewrite the expression.

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

Multiply $4$ by $- 1$ .

$x^{2} - 4 = 0$

Step 3

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 4

Substitute the values $a = 1$ , $b = 0$ , and $c = - 4$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (1 \cdot - 4)}}{2 \cdot 1}$

Step 5

Simplify.

Simplify the numerator.

Raising $0$ to any positive power yields $0$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 1 \cdot - 4}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 4$ .

Multiply $- 4$ by $1$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot - 4}}{2 \cdot 1}$

Multiply $- 4$ by $- 4$ .

$x = \frac{0 \pm \sqrt{0 + 16}}{2 \cdot 1}$

Add $0$ and $16$ .

$x = \frac{0 \pm \sqrt{16}}{2 \cdot 1}$

Rewrite $16$ as $4^{2}$ .

$x = \frac{0 \pm \sqrt{4^{2}}}{2 \cdot 1}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{0 \pm 4}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{0 \pm 4}{2}$

Simplify $\frac{0 \pm 4}{2}$ .

$x = \pm 2$

Step 6

The final answer is the combination of both solutions.

$x = 2, - 2$