Transcript Solving Quadratic Equations by Completing the Square

SOLVING QUADRATIC
EQUATIONS BY
COMPLETING THE SQUARE
PERFECT SQUARE TRINOMIALS
 Examples
 x2
+ 6x + 9
 x2 - 10x + 25
 x2 + 12x + 36
 X2
CREATING A PERFECT
SQUARE TRINOMIAL
+ 14x + ____
 Find the constant term by squaring
half of b
 (14/2)2
X2 + 14x + 49
 Factored this becomes (x+7)2
14/2 – half of b
PERFECT SQUARE TRINOMIALS
 Create
perfect
square trinomials.
 x2 + 20x + ___
 x2 - 4x + ___
 x2 + 5x + ___
100
4
25/4
TO SOLVE BY COMPLETING THE
SQUARE
If a quadratic equation does not factor we can
solve it by two different methods
 1.) Completing the Square (today’s lesson)
 2.) Quadratic Formula (tomorrow’s lesson)

STEPS TO SOLVE BY COMPLETING THE SQUARE
1.) If the quadratic does not factor, move c to the
other side of the equation, leave space on left!
x²-4x -7 =0
x²-4x
=7
2.) Make the left side a perfect square trinomial and
add number to both sides of equation
x² -4x
4/2= 2²=4
x² -4x +4 = 7 +4
3.)Factor your trinomial square
(x-2)² =11
4.)Solve by square roots method
x-2 = ±√11
x = 2±√11
EXAMPLE
Solve the following
equation by
completing the
square:
Step 1: Move
quadratic term, and
linear term to left
side of the equation
x 2  8 x  20  0
x  8 x  20
2
SOLVING QUADRATIC EQUATIONS
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.
x  8x 
2
BY
=20 +
1
 (8)  4 then square it, 42  16
2
x  8 x  16  20 16
2
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.
x  8 x  16  20 16
2
( x  4)  36
2
SOLVING QUADRATIC EQUATIONS BY
COMPLETING THE SQUARE
Step 4:
Take the
square root
of each
side
( x  4)  36
2
( x  4)  6
SOLVING QUADRATIC EQUATIONS BY
COMPLETING THE SQUARE
Step 5: Set
up the two
possibilities
and solve
x  4  6
x  4  6 and x  4  6
x  10 and x=2
x  5x  3  0
2
2
2

5
5

x  5x  2   3   2 
2
2
5  37

x  
2
4

5  37
x 
2
2
5  37
x
2
SOLVING QUADRATIC EQUATIONS
COMPLETING THE SQUARE
BY
Try the following examples. Do your work on your paper and then check
your answers.
1.  9, 7 
1. x 2  2 x  63  0
2.(6, 14)
2. x 2  8 x  84  0
3.  3,8 
3. x  5 x  24  0
2
4. x 2  7 x  13  0
 7  i 3 
4. 

2

