Sec 1.7 –Revisiting Quadratics
Square Root & Complete the Square Method
Name:
Solve the following QUADRATIC EQUATIONS using the SQUARE ROOT METHOD:
2
1. 4w  9  0
2
2. y  36  0
2
3. 4m  48  0
5. 3  x  5  29  2
1

2  a  1  35  5

6.  2
2
4.  b  2   36
2
2
Completing the Square (BASIC):
x2  6 x  25  0
x2  6 x  25  0
-25
x2  6 x
½ of
6
:Move constant to the other side
-25
 25
3
Square
3
9
x2  6 x  9  16
 x  3 x  3  16
2
 x  3  16
 x  3
x 2  6 x  9  25  9
2
 16
x  3   4i
–3
–3
x  3  4i
M. Winking
Unit 1-7 page 18
Add 25
9 toto
Add
both
sides
both sides
:Easily Factors
:Can be re-written
:Take the square root of both sides
:Don’t forget

:Isolate the variable
Solve the following by completing the square.
7.
x2  10 x  29  0
8.
x2  8x  16  0
9.
x2  4 x  22  0
10.
x2  5x  12  0
Completing the Square (INTERMEDIATE):
4 x2  8x  5  0
4 x2  8x  5  0
-5
4 x2  8x
 5
x2  2 x
  54
4
½ of
-2
:Move constant to the other side
-5
4
-1
x 2  2 x  1   14
 x 1 x  1   14
2
 x  1   14
2
   14
x  1   12 i
+1
x 2  2 x  1   54  1
Square
(-1)
1
 x  1
:Divide both sides by the Lead Coefficient
:Easily Factors
:Can be re-written
:Take the square root of both sides
:Don’t forget

:Isolate the variable
+1
x  1  12 i
M. Winking
Add 25
1 toto
Add
both sides
both
sides
Unit 1-7 page 19
(4)
Solve the following by completing the square.
11.
4 x2  24 x  37  0
12.
2 x2  20 x  53  0
Completing the Square (ADVANCED):
2 x2  9 x  21  0
2 x2  9 x  21  0
:Move constant to the other side
2 x2  9 x
:Divide both sides by the Lead Coefficient
-21 -21
 21
2
2
x 2  92 x
9
2
Half of
−
9 1
− ∙
2 2
9
−
4
=
  212
Square
−
9
4
81
16
x 2  92 x 
Realize that − 94 is
perfect for
factoring because:
−
9
4
+
9
(− 4)
−
9
4
=
and
9
(− 4) =
−
x 2  92 x 
9 2
−
81
16
81
16
9
2
81
Add 25
to
Add
16 to
both sides
both
sides
81
(− 4) = 16
81
16
  212 
87
  16
:Can be factored
 x  94  x  94    1687
:Can be re-written
9
2
81
16
 x  94 
2
 x  94 
2
87
  16
87
   16
x  94  
9
+
4
x
:Take the square root of both sides
9
+
4
9
4

M. Winking
87
4
87
4
:Don’t forget
:Isolate the variable
i
i 

9i 87
4
Unit 1-7 page 20
(2)
Solve the following by completing the square.
7.
2 x2  10 x  15  0
9.
2 x2  15x  30  0
8.
3x2  12 x  16  0
10.
M. Winking
Unit 1-7 page 21
4 x2  5x  3  0