Solve by Factoring x^2-9x-22=0

$x^{2} - 9 x - 22 = 0$

Step 1

Factor $x^{2} - 9 x - 22$ 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 $- 22$ and whose sum is $- 9$ .

$- 11, 2$

Write the factored form using these integers.

$(x - 11) (x + 2) = 0$

Step 2

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

$x - 11 = 0$

$x + 2 = 0$

Step 3

Set $x - 11$ equal to $0$ and solve for $x$ .

Set $x - 11$ equal to $0$ .

$x - 11 = 0$

Add $11$ to both sides of the equation.

$x = 11$

Step 4

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.

$x = - 2$

Step 5

The final solution is all the values that make $(x - 11) (x + 2) = 0$ true.

$x = 11, - 2$

Solve by Factoring x^2-9x-22=0

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