Solve by Factoring x^2+19x=-84

$x^{2} + 19 x = - 84$

Step 1

Add $84$ to both sides of the equation.

$x^{2} + 19 x + 84 = 0$

Step 2

Factor $x^{2} + 19 x + 84$ 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 $84$ and whose sum is $19$ .

$7, 12$

Write the factored form using these integers.

$(x + 7) (x + 12) = 0$

Step 3

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

$x + 7 = 0$

$x + 12 = 0$

Step 4

Set $x + 7$ equal to $0$ and solve for $x$ .

Set $x + 7$ equal to $0$ .

$x + 7 = 0$

Subtract $7$ from both sides of the equation.

$x = - 7$

Step 5

Set $x + 12$ equal to $0$ and solve for $x$ .

Set $x + 12$ equal to $0$ .

$x + 12 = 0$

Subtract $12$ from both sides of the equation.

$x = - 12$

Step 6

The final solution is all the values that make $(x + 7) (x + 12) = 0$ true.

$x = - 7, - 12$

Solve by Factoring x^2+19x=-84

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