Solve by Factoring x^2+11x+28=0

$x^{2} + 11 x + 28 = 0$

Step 1

Factor $x^{2} + 11 x + 28$ 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 $28$ and whose sum is $11$ .

$4, 7$

Write the factored form using these integers.

$(x + 4) (x + 7) = 0$

Step 2

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

$x + 4 = 0$

$x + 7 = 0$

Step 3

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.

$x = - 4$

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

The final solution is all the values that make $(x + 4) (x + 7) = 0$ true.

$x = - 4, - 7$

Solve by Factoring x^2+11x+28=0

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