Transcript Solving Quadratic Equations by Completing the Square

Factoring Polynomials
by Completing the
Square
Perfect Square Trinomials
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Examples
x2 + 6x + 9
x2 - 10x + 25
x2 + 12x + 36
Creating a Perfect
Square Trinomial
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In the following perfect square
trinomial, the constant term is
missing.
X2 + 14x + ____
Find the constant term by
squaring half the coefficient of
the linear term.
(14/2)2
X2 + 14x + 49
Perfect Square Trinomials
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Create perfect
square trinomials.
x2 + 20x + ___
x2 - 4x + ___
x2 + 5x + ___
100
4
25/4
Factoring Quadratics by
Completing the Square
Factor by completing
the square:
x +8x - 20
2
Step 1: First take the
coefficient of the
linear term, divide it
by 2, and then
square it. This gives
16 - (8/2)2
x +8x - 20
2
Factoring by Completing the
Square
Step 2: Add and subtract 16 just after
the linear term. Therefore, you did
not change the value of the
expression.
x +8x +16 -16+20
2
Factoring by Completing the
Square
Step 3: Use brackets to group the first
three terms – This is your perfect
square trinomial.
(x +8x + 16)-16+20
2
Factoring by Completing the
Square
Step 3: Factor the perfect square
trinomial and simplify the rest.
(x +8x + 16)-16+20
2
(x + 4)2 + 4
X2 – 12x + 4
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Step 1: First take the coefficient of the linear term, divide it
by 2, and then square it.
Step 2: Add and subtract 16 just after the linear term.
Therefore, you did not change the value of the
expression.
Step 3: Use brackets to group the first three terms –
This is your perfect square trinomial.
Factor by Completing the
Square
Step 1: First take the coefficient of the linear
term, divide it by 2, and then square it.
Step 2: Add and subtract 16 just after the
linear term. Therefore, you did not change the
value of the expression.
Step 3: Use brackets to group the first three
terms – This is your perfect square trinomial.
7
x - x +6
2
2
Solving Quadratic Equations by
Completing the Square
Step 4:
Take the
square
root of
each side
7 2
47
(x  ) 
4
16
7
47
(x  )  
4
4
7 i 47
x 
4
4
7  i 47
x
4
Solving Quadratic Equations by
Completing the Square
Try the following examples. Do your work on your paper and then check
your answers.
1. x  2 x  63  0
2
2. x  8 x  84  0
2
3. x  5 x  24  0
2
4. x  7 x  13  0
2
5. 3 x 2 5 x  6  0
1.  9, 7 
2.(6, 14)
3.  3,8 
 7  i 3 
4. 

2


 5  i 47 
5. 

6

