Question

Solve x2 + 14x = −24 by completing the square. What is the solution set of the equation? a. {−12, −2} b. {−7, 7} c. {−6, −4} d. {−5, 5}

Answer 1

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Answer 2

First, rearrange the equation so that only zero will be on the right side:

x^2 + 14x +24 = 0

Let the coefficients be:

a = 1

b = 14

c = 24

To complete the square, add (b/2)^2 to both sides of the equation:

(b/2)^2 = 49

x^2 + 14x + 49 + 24 = 49

x^2 + 14x + 49 = 25

(x+7)^2 = 25

Therefore, the solution set of the equation is {-12, -2}