Solve for a a^2+11a=-18

$a^{2} + 11 a = - 18$

Step 1

Add $18$ to both sides of the equation.

$a^{2} + 11 a + 18 = 0$

Step 2

Factor $a^{2} + 11 a + 18$ using the AC method.

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 $18$ and whose sum is $11$ .

$2, 9$

Write the factored form using these integers.

$(a + 2) (a + 9) = 0$

Step 3

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

$a + 2 = 0$

$a + 9 = 0$

Step 4

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

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

$a + 2 = 0$

Subtract $2$ from both sides of the equation.

$a = - 2$

Step 5

Set $a + 9$ equal to $0$ and solve for $a$ .

Set $a + 9$ equal to $0$ .

$a + 9 = 0$

Subtract $9$ from both sides of the equation.

$a = - 9$

Step 6

The final solution is all the values that make $(a + 2) (a + 9) = 0$ true.

$a = - 2, - 9$

Solve for a a^2+11a=-18

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