Solve by Factoring x^2+31=-14x-9

$x^{2} + 31 = - 14 x - 9$

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

Add $14 x$ to both sides of the equation.

$x^{2} + 31 + 14 x = - 9$

Add $9$ to both sides of the equation.

$x^{2} + 31 + 14 x + 9 = 0$

Add $31$ and $9$ .

$x^{2} + 14 x + 40 = 0$

Factor $x^{2} + 14 x + 40$ 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 $40$ and whose sum is $14$ .

$4, 10$

Write the factored form using these integers.

$(x + 4) (x + 10) = 0$

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

$x + 4 = 0$

$x + 10 = 0$

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

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

$x + 4 = 0$

Subtract $4$ from both sides of the equation.

$x = - 4$

Set $x + 10$ equal to $0$ and solve for $x$ .

Set $x + 10$ equal to $0$ .

$x + 10 = 0$

Subtract $10$ from both sides of the equation.

$x = - 10$

The final solution is all the values that make $(x + 4) (x + 10) = 0$ true.

$x = - 4, - 10$

Solve by Factoring x^2+31=-14x-9

Related Questions

Support LCMGCF.com by disabling your adblocker.