Pre-Algebra Examples

$0 = x^{2} + 7 x + 12$

Step 1

Rewrite the equation as $x^{2} + 7 x + 12 = 0$ .

$x^{2} + 7 x + 12 = 0$

Step 2

Factor $x^{2} + 7 x + 12$ using the AC method.

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Step 2.1

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 $12$ and whose sum is $7$ .

$3, 4$

Step 2.2

Write the factored form using these integers.

$(x + 3) (x + 4) = 0$

Step 3

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

$x + 3 = 0$

$x + 4 = 0$

Step 4

Set $x + 3$ equal to $0$ and solve for $x$ .

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Step 4.1

Set $x + 3$ equal to $0$ .

$x + 3 = 0$

Step 4.2

Subtract $3$ from both sides of the equation.

$x = - 3$

Step 5

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

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Step 5.1

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

$x + 4 = 0$

Step 5.2

Subtract $4$ from both sides of the equation.

$x = - 4$

Step 6

The final solution is all the values that make $(x + 3) (x + 4) = 0$ true.

$x = - 3, - 4$