Solve for s s^2+12s=-32

$s^{2} + 12 s = - 32$

Step 1

Add $32$ to both sides of the equation.

$s^{2} + 12 s + 32 = 0$

Step 2

Factor $s^{2} + 12 s + 32$ 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 $32$ and whose sum is $12$ .

$4, 8$

Write the factored form using these integers.

$(s + 4) (s + 8) = 0$

Step 3

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

$s + 4 = 0$

$s + 8 = 0$

Step 4

Set $s + 4$ equal to $0$ and solve for $s$ .

Set $s + 4$ equal to $0$ .

$s + 4 = 0$

Subtract $4$ from both sides of the equation.

$s = - 4$

Step 5

Set $s + 8$ equal to $0$ and solve for $s$ .

Set $s + 8$ equal to $0$ .

$s + 8 = 0$

Subtract $8$ from both sides of the equation.

$s = - 8$

Step 6

The final solution is all the values that make $(s + 4) (s + 8) = 0$ true.

$s = - 4, - 8$

Solve for s s^2+12s=-32

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