Precalculus Examples

$a^{2} + 4 a - 12 = 0$

Step 1

Factor $a^{2} + 4 a - 12$ using the AC method.

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Step 1.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 12$ and whose sum is $4$ .

$- 2, 6$

Step 1.2

Write the factored form using these integers.

$(a - 2) (a + 6) = 0$

Step 2

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$a - 2 = 0$

$a + 6 = 0$

Step 3

Set $a - 2$ equal to $0$ and solve for $a$ .

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Step 3.1

Set $a - 2$ equal to $0$ .

$a - 2 = 0$

Step 3.2

Add $2$ to both sides of the equation.

$a = 2$

Step 4

Set $a + 6$ equal to $0$ and solve for $a$ .

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Step 4.1

Set $a + 6$ equal to $0$ .

$a + 6 = 0$

Step 4.2

Subtract $6$ from both sides of the equation.

$a = - 6$

Step 5

The final solution is all the values that make $(a - 2) (a + 6) = 0$ true.

$a = 2, - 6$