Unit 3-Day 5:
Solving Quadratic Equations by
Completing the Square
Objective:
To solve Quadratic Equations by
Completing the Square
Unit 3, Day 5 Assignment: Pg. 286-87: 23, 25,
33, 35, 47, 49, 55, 85
Honors: In addition to above, complete 39
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Completing the Square
What is completing the square used for?
Completing the square is used for all those
non factorable problems!!
It is used to solve these equations for the
variable.
The first step in completing the square is
transform the quadratic equation into an
equation that has a Perfect Square Trinomial
Perfect Square Trinomials
a  2ab  b   a  b 
2
2
a  2ab  b   a  b 
2
2
Examples
x2 + 6x + 9
x2 - 10x + 25
x2 + 12x + 36
2
2
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Creating a Perfect Square Trinomial
• In the following perfect square trinomial the
constant term is missing:
• x2 + 14x + ___
By adding 49, we will make a perfect square trinomial
x2 + 14x + 49
Factor: ( x  7)( x  7)  ( x  7)
• But how did we come up with 49?!!!
2
Rules for Completing the Square
Given
x +bx
2
2
b
x +bx +  
2
2
2
Factors into:
b

x + 
2

Examples: Create perfect square
trinomials.
x2 + 20x + ___
x2 - 4x + ___
x2 + 5x + ___
Solving a Quadratic Equation When
2
x
the Coefficient of is 1.
Solve
x  8 x  20  0
2
x  8 x  20 Start by isolating the x terms.
2
x  8x 
2
 20 
Complete the Square
Add to both sides
(We will finish rest in class)
Examples
Solve by completing the square
When the leading coefficient is 1
x 2  10 x  3  0
What if the leading coefficient is not 1
3x2  6 x  12  0