Solve Using the Quadratic Formula 4x^2-8=0

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Algebra

$4 x^{2} - 8 = 0$

Use the quadratic formula to find the solutions.

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

Substitute the values $a = 4$ , $b = 0$ , and $c = - 8$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (4 \cdot - 8)}}{2 \cdot 4}$

Simplify.

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Simplify the numerator.

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

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

Multiply $- 4$ by $4$ .

$x = \frac{0 \pm \sqrt{0 - 16 \cdot - 8}}{2 \cdot 4}$

Multiply $- 16$ by $- 8$ .

$x = \frac{0 \pm \sqrt{0 + 128}}{2 \cdot 4}$

Add $0$ and $128$ .

$x = \frac{0 \pm \sqrt{128}}{2 \cdot 4}$

Rewrite $128$ as $8^{2} \cdot 2$ .

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Factor $64$ out of $128$ .

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

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

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

Pull terms out from under the radical.

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

Multiply $2$ by $4$ .

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

Simplify $\frac{0 \pm 8 \sqrt{2}}{8}$ .

$x = \pm \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{2}$

Decimal Form:

$x = 1.41421356 \dots, - 1.41421356 \dots$

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