Page 671 - Algebra 1

Example
2
Solving Quadratic Equations by Factoring
Find the roots.
a. x2+2x=8 SOLUTION
x2 + 2x = 8 x2 +2x-8=0 (x + 4)(x - 2) = 0
Settheequationequalto0. Factor.
Hint
Standard form for the equation is
ax2 +bx+c=0.
Use the Zero Product Property to solve the equation.
x + 4 = 0 x = -4
Check
x2 +2x=8 (-4)2 +2(-4) 8 16 - 8 8
8=8 ✓ The roots are -4 and 2.
b. 7x2-6=19x SOLUTION
7x2 -6=19x 7x2 -19x-6=0 (7x + 2)(x - 3) = 0
7x + 2 = 0 7x = -2
x - 2 = 0 x = 2
Set each factor equal to zero. Solve each equation for x.
x = - _2 7
Check
7x2 -6= 19x _2 2
7x2 -6=19x 7 ( 3 ) 2 - 6 1 9 ( 3 ) 63 - 6 57
57=57 ✓
_2 7(-7) - 6 19(-7)
_4 _38 (7)-6 -7
__ -38=-38 ✓
77
The roots are -_2 and 3. 7
x2 +2x=8 (2)2 +2(2) 8 4 + 4 8
8=8 ✓
Settheequationequalto0. Factor.
x - 3 = 0 x = 3
Set each factor equal to zero. Solve each equation for x.
656 Saxon Algebra 1