solvingquadraticsbycompletingthesquare-131104055048-phpapp01.ppt

Solving quadratic equation by completing the square

1. Solving Quadratic
Equations by
Completing the Square

2. Perfect Square Trinomials
Examples
x
2
+ 6x + 9
x
2
- 10x + 25
x
2
+ 12x + 36

3. Creating a Perfect
Square Trinomial
In the following perfect square
trinomial, the constant term is
missing. X
2

+ 14x + ____
Find the constant term by squaring
half the coefficient of the linear
term.
(14/2)
2
X
2

+ 14x + 49

4. Perfect Square Trinomials
Create perfect
square trinomials.
x
2
+ 20x + ___
x
2
- 4x + ___
x
2
+ 5x + ___
100
4
25/4

5. Solving Quadratic Equations
by Completing the Square
Solve the following
equation by
completing the
square:
Step 1: Move
quadratic term, and
linear term to left
side of the
equation
2
8 20 0x x  
2
8 20x x 

6. Solving Quadratic Equations
by Completing the Square
Step 2: Find the term
that completes the square
on the left side of the
equation. Add that term
to both sides.
2
8 =20 + x x  
21
( ) 4 then square it, 4 16
2
8  
2
8 2016 16x x   

7. Solving Quadratic Equations
by Completing the Square
Step 3: Factor
the perfect
square trinomial
on the left side
of the equation.
Simplify the
right side of the
equation.
2
8 2016 16x x   
2
( 4)( 4) 36
( 4) 36
x x
x
  
 

8. Solving Quadratic Equations
by Completing the Square
Step 4:
Take the
square
root of
each side
2
( 4) 36x 
( 4) 6x 

9. Solving Quadratic Equations
by Completing the Square
Step 5: Set
up the two
possibilities
and solve
4 6
4 6 an

d 4 6
10 and 2 x=
x
x x
x
 


   

10. Completing the Square-Example #2
Solve the following
equation by completing
the square:
Step 1: Move quadratic
term, and linear term to
left side of the equation,
the constant to the right
side of the equation.
2
2 7 12 0x x  
2
2 7 12x x 

11. Solving Quadratic Equations
by Completing the Square
Step 2: Find the term
that completes the square
on the left side of the
equation. Add that term
to both sides.
The quadratic coefficient
must be equal to 1 before
you complete the square, so
you must divide all terms
by the quadratic
coefficient first.
2
2
2
2 7
2
2 2 2
7 12

7
2
=-12 +

6


x x
x x
xx
 
 
 
 
  
 
 
2
1 7 7 49
( ) then square it,
2 624 4 1
7  
  
 
 
2 49 49
16 1
7
6
2 6
x x   

12. Solving Quadratic Equations
by Completing the Square
Step 3: Factor
the perfect
square trinomial
on the left side
of the equation.
Simplify the
right side of the
equation.
2
2
2
7
6
2
7 96 49
4 16 16
7 47
4
49 49
16 1
16
6
x x
x
x
   
 
  
 
 
 
 
 
 

13. Solving Quadratic Equations by
Completing the Square
Step 4:
Take the
square
root of
each side
27 47
( )
4 16
x

 
7 47
( )
4 4
7 47
4 4
7 47
4
x
i
x
i
x

 
 



14. Solving Quadratic Equations by
Completing the Square
2
2
2
2
2
1. 2 63 0
2. 8 84 0
3. 5 24 0
4. 7 13 0
5. 3 5 6 0
x x
x x
x x
x x
x x
  
  
  
  
  
Try the following examples. Do your work on your paper and then check
your answers.

15. Solving Quadratic Equations by
Completing the Square
2
2
2
2
2
1. 2 63 0
2. 8 84 0
3. 5 24 0
4. 7 13 0
5. 3 5 6 0
x x
x x
x x
x x
x x
  
  
  
  
  
Try the following examples. Do your work on your paper and then check
your answers.


1. 9,7
2.(6, 14)
3. 3,8
7 3
4.
2
5 47
5.
6
i
i



  
 
 
 
  
 
 
 