Question

Solve x^2 +14x = -24 by completing the square. Which is the solution set of the equation?

Answer 1

Start with x^2 +14x = -24,

Find HALF the value of 14:  7
Square this:  49
Add 49, and then subtract 49:        x^2 + 14x + 49 - 49 = -24  We have a
                                                                                             perfect square
Rewrite the quadratic as the sq. of a binomial:                    trinomial on
                                                                                              the left
                                                         (x+7)^2 = 25

Take the sqrt of both sides:  x+7 = plus or minus 5

Then x = -2 and x = -12