Pre-Algebra Examples

$- p^{2} - 12 p - 36 = 0$

Step 1

Factor the left side of the equation.

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Step 1.1

Factor $- 1$ out of $- p^{2} - 12 p - 36$ .

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Step 1.1.1

Factor $- 1$ out of $- p^{2}$ .

$- (p^{2}) - 12 p - 36 = 0$

Step 1.1.2

Factor $- 1$ out of $- 12 p$ .

$- (p^{2}) - (12 p) - 36 = 0$

Step 1.1.3

Rewrite $- 36$ as $- 1 (36)$ .

$- (p^{2}) - (12 p) - 1 \cdot 36 = 0$

Step 1.1.4

Factor $- 1$ out of $- (p^{2}) - (12 p)$ .

$- (p^{2} + 12 p) - 1 \cdot 36 = 0$

Step 1.1.5

Factor $- 1$ out of $- (p^{2} + 12 p) - 1 (36)$ .

$- (p^{2} + 12 p + 36) = 0$

Step 1.2

Factor using the perfect square rule.

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Step 1.2.1

Rewrite $36$ as $6^{2}$ .

$- (p^{2} + 12 p + 6^{2}) = 0$

Step 1.2.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$12 p = 2 \cdot p \cdot 6$

Step 1.2.3

Rewrite the polynomial.

$- (p^{2} + 2 \cdot p \cdot 6 + 6^{2}) = 0$

Step 1.2.4

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = p$ and $b = 6$ .

$- {(p + 6)}^{2} = 0$

Step 2

Divide each term in $- {(p + 6)}^{2} = 0$ by $- 1$ and simplify.

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Step 2.1

Divide each term in $- {(p + 6)}^{2} = 0$ by $- 1$ .

$\frac{- {(p + 6)}^{2}}{- 1} = \frac{0}{- 1}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Dividing two negative values results in a positive value.

$\frac{{(p + 6)}^{2}}{1} = \frac{0}{- 1}$

Step 2.2.2

Divide ${(p + 6)}^{2}$ by $1$ .

${(p + 6)}^{2} = \frac{0}{- 1}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $0$ by $- 1$ .

${(p + 6)}^{2} = 0$

Step 3

Set the $p + 6$ equal to $0$ .

$p + 6 = 0$

Step 4

Subtract $6$ from both sides of the equation.

$p = - 6$