Solve by Factoring x^2+3x-28=0

$x^{2} + 3 x - 28 = 0$

Factor $x^{2} + 3 x - 28$ using the AC method.

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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 $3$ .

$- 4, 7$

Write the factored form using these integers.

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

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

$x - 4 = 0$

$x + 7 = 0$

Set the first factor equal to $0$ and solve.

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Set the first factor equal to $0$ .

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

Set the next factor equal to $0$ and solve.

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Set the next factor equal to $0$ .

$x + 7 = 0$

Subtract $7$ from both sides of the equation.

$x = - 7$

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

$x = 4, - 7$

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