Finite Math Examples

$- 4 x^{2} - 8 x^{2} + 3$

Step 1

Set $- 4 x^{2} - 8 x^{2} + 3$ equal to $0$ .

$- 4 x^{2} - 8 x^{2} + 3 = 0$

Step 2

Simplify the left side.

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Step 2.1

Subtract $8 x^{2}$ from $- 4 x^{2}$ .

$- 12 x^{2} + 3 = 0$

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 $a = - 12$ , $b = 0$ , and $c = 3$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (- 12 \cdot 3)}}{2 \cdot - 12}$

Step 5

Simplify.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot - 12 \cdot 3}}{2 \cdot - 12}$

Step 5.1.2

Multiply $- 4 \cdot - 12 \cdot 3$ .

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Step 5.1.2.1

Multiply $- 4$ by $- 12$ .

$x = \frac{0 \pm \sqrt{0 + 48 \cdot 3}}{2 \cdot - 12}$

Step 5.1.2.2

Multiply $48$ by $3$ .

$x = \frac{0 \pm \sqrt{0 + 144}}{2 \cdot - 12}$

Step 5.1.3

Add $0$ and $144$ .

$x = \frac{0 \pm \sqrt{144}}{2 \cdot - 12}$

Step 5.1.4

Rewrite $144$ as $12^{2}$ .

$x = \frac{0 \pm \sqrt{12^{2}}}{2 \cdot - 12}$

Step 5.1.5

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

$x = \frac{0 \pm 12}{2 \cdot - 12}$

Step 5.2

Multiply $2$ by $- 12$ .

$x = \frac{0 \pm 12}{- 24}$

Step 5.3

Simplify $\frac{0 \pm 12}{- 24}$ .

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

Step 6

The final answer is the combination of both solutions.

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