Solve by Factoring x^2+x=-9x-16

$x^{2} + x = - 9 x - 16$

Move all the expressions to the left side of the equation.

Add $9 x$ to both sides of the equation.

$x^{2} + x + 9 x = - 16$

Add $16$ to both sides of the equation.

$x^{2} + x + 9 x + 16 = 0$

Add $x$ and $9 x$ .

$x^{2} + 10 x + 16 = 0$

Factor $x^{2} + 10 x + 16$ 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 $16$ and whose sum is $10$ .

$2, 8$

Write the factored form using these integers.

$(x + 2) (x + 8) = 0$

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

$x + 2 = 0$

$x + 8 = 0$

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

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

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

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

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

$x + 8 = 0$

Subtract $8$ from both sides of the equation.

$x = - 8$

The final solution is all the values that make $(x + 2) (x + 8) = 0$ true.

$x = - 2, - 8$

Solve by Factoring x^2+x=-9x-16

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