A.5 Methods for
Solving Equations
Failures are finger posts on the road to achievement.
-C. S. Lewis

Solving Quadratic Equations: GCF
Solve the equation.
x 2  2x
Solve the equation.
x 3  6x 2

Solving Quadratic Equations: Factoring
Solve the equation.
x 2  12  x
Solve the equation.
3
2
x  6x  9x  0
Solving Equations: Factoring
Solve the equation.
3x 3  4 x 2  27 x  36  0
Solve ANY Quadratic
If a quadratic can’t be factored. There are two
methods that can be used to solve any quadratic
equation:
1. Completing the Square
2. Quadratic Formula
−𝒃 ± 𝒃𝟐 − 𝟒𝒂𝒄
𝒙=
𝟐𝒂
Completing the Square (a = 1)
x 2  6x  4  0
x 2  6x
 4
Step 1: Move c to the other side
Step 2:


x  6x  9  5
2
b 2
Add   to
2 
Step 
3: Rewrite the left side as
2
the perfect square  b 
x  
 2 
(x  3) 2  5

both sides
Step 4:
both sides and solve!



Completing the Square (a ≠ 1)
Solve the equation.
4 x 2  8x  1  0

Equations in Quadratic Form
The following equation resembles quadratic form. Let’s solve it!
2x 4  9x 2  35  0

Equations in Quadratic Form
How can we solve this equation without multiplying it out?
(3x  4)2  6(3x  4) 16  0

Solving Rational Equations
Practice with your groups!
Pg 998 #82, 86, 88, 90, 110
A.5 Methods for
Homework #5: p.998
Solving Equations
#81 – 89 Odd
#93-97 odd
#105 & 109 (complete the
square and quadratic formula)
Failures are finger posts on the road to achievement.
-C. S. Lewis