College Algebra & Trigonometry, 2018a

52 CHAPTER 1. ALGEBRA REVIEW
The fact that the roots of this equation were rational numbers means that the
equation could have been solved by factoring.
0=5x 2 +33x +40
0=(5x +8)(x +5)
5x +8=0 x +5=0
5x = −8
x = −5
x = −1.6
Example
Solve for x.
(x − 2) 2 +3(4x − 1)(x +1)=7(x +1)(x − 1)
x 2 − 4x +4+3(4x 2 +3x − 1) = 7(x 2 − 1)
x 2 − 4x +4+12x 2 +9x − 3=7x 2 − 7
13x 2 +5x +1=7x 2 − 7
6x 2 +5x +8=0
a =6,b=5,c=8
x ≈−0.416 ± 1.077i ≈− 5
12 ± 1.077i