Solve Using the Quadratic Formula 4x^2-28=0

$4 x^{2} - 28 = 0$

Step 1

Use the quadratic formula to find the solutions.

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

Step 2

Substitute the values $a = 4$ , $b = 0$ , and $c = - 28$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (4 \cdot - 28)}}{2 \cdot 4}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 4 \cdot - 28}}{2 \cdot 4}$

Multiply $- 4 \cdot 4 \cdot - 28$ .

Multiply $- 4$ by $4$ .

$x = \frac{0 \pm \sqrt{0 - 16 \cdot - 28}}{2 \cdot 4}$

Multiply $- 16$ by $- 28$ .

$x = \frac{0 \pm \sqrt{0 + 448}}{2 \cdot 4}$

Add $0$ and $448$ .

$x = \frac{0 \pm \sqrt{448}}{2 \cdot 4}$

Rewrite $448$ as $8^{2} \cdot 7$ .

Factor $64$ out of $448$ .

$x = \frac{0 \pm \sqrt{64 (7)}}{2 \cdot 4}$

Rewrite $64$ as $8^{2}$ .

$x = \frac{0 \pm \sqrt{8^{2} \cdot 7}}{2 \cdot 4}$

Pull terms out from under the radical.

$x = \frac{0 \pm 8 \sqrt{7}}{2 \cdot 4}$

Multiply $2$ by $4$ .

$x = \frac{0 \pm 8 \sqrt{7}}{8}$

Simplify $\frac{0 \pm 8 \sqrt{7}}{8}$ .

$x = \pm \sqrt{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{7}$

Decimal Form:

$x = 2.64575131 \dots, - 2.64575131 \dots$