Algebra Examples

$- x^{2} - 36$

Step 1

Use the quadratic formula to find the roots for $- x^{2} - 36 = 0$

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Use the quadratic formula to find the solutions.

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

Substitute the values $a = - 1$ , $b = 0$ , and $c = - 36$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (- 1 \cdot - 36)}}{2 \cdot - 1}$

Simplify.

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Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot - 1 \cdot - 36}}{2 \cdot - 1}$

Multiply $- 4 \cdot - 1 \cdot - 36$ .

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Multiply $- 4$ by $- 1$ .

$x = \frac{0 \pm \sqrt{0 + 4 \cdot - 36}}{2 \cdot - 1}$

Multiply $4$ by $- 36$ .

$x = \frac{0 \pm \sqrt{0 - 144}}{2 \cdot - 1}$

Subtract $144$ from $0$ .

$x = \frac{0 \pm \sqrt{- 144}}{2 \cdot - 1}$

Rewrite $- 144$ as $- 1 (144)$ .

$x = \frac{0 \pm \sqrt{- 1 \cdot 144}}{2 \cdot - 1}$

Rewrite $\sqrt{- 1 (144)}$ as $\sqrt{- 1} \cdot \sqrt{144}$ .

$x = \frac{0 \pm \sqrt{- 1} \cdot \sqrt{144}}{2 \cdot - 1}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \frac{0 \pm i \cdot \sqrt{144}}{2 \cdot - 1}$

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

$x = \frac{0 \pm i \cdot \sqrt{12^{2}}}{2 \cdot - 1}$

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

$x = \frac{0 \pm i \cdot 12}{2 \cdot - 1}$

Move $12$ to the left of $i$ .

$x = \frac{0 \pm 12 i}{2 \cdot - 1}$

Multiply $2$ by $- 1$ .

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

Simplify $\frac{0 \pm 12 i}{- 2}$ .

$x = \pm 6 i$

Step 2

Find the factors from the roots, then multiply the factors together.

$- (x - (6 i)) (x - (- 6 i))$

Step 3

Simplify the factored form.

$- (x - 6 i) (x + 6 i)$