Question

What are the solutions of the quadratic equation?

x2 + 11x = –24 (Multiple Choice)

◘ -3, -8
◘ -3, 8
◘ 3, -8
◘ 3, 8

Answer 1

We have x^2 + 2 · x · (11/2) + (11/2)^2 = - 24 + (11/2)^2;
Then, ( x + 11/2 )^2 = -24 + 121/4;
( x + 11/2 )^2 + 96/4 - 121/4 = 0;
( x + 11/2 )^2 - 25 / 4 = 0;
( x + 11/2 )^2 - (5/2)^2 = 0;
( x + 11/2 - 5/2)·( x + 11/2 + 5/2 ) = 0;
( x + 6/2 )·( x + 16/2 ) = 0;
( x + 3 )· ( x + 8 ) = 0;
x = - 3 or x = -8;
The first choice is the correct answer.

Answer 2

Original equation:
x^2 + 11x = -24
Move everything to the left hand side of the equation. To do this, add 24 to each side.
x^2 + 11x + 24 = 0
Now figure out a combination of two numbers that when added equals 11 but when multiplied equals 24. The answer is 8 and 3.
(x + 8)(x + 3) = 0
You can check the result by doing FOIL.
There are two values for which the equation works: x = -8 and x = -3.