These steps show how to derive the quadratic formula by completing the square. Some of the expressions are missing.
a
x
2
b
x
c
0
x
2
b
a
x
c
a
Step 1
0
Step 1
x
2
b
a
x
Step 2
c
a
Step 2
x
2
b
a
x
Step 3
c
a
b
2
a
2
Step 3
x
b
2
a
2
Step 4
c
a
b
2
a
2
Step 4
Step 5
±
c
a
b
2
a
2
Step 5
x
Step 6
b
2
a
±
c
a
b
2
a
2
Step 6
x
Step 7
b
2
a
±
2
a
c
a
b
2
a
2
2
a
Step 7
x
Step 8
b
±
2
a
c
a
b
2
a
2
2
a
Step 8
x
Step 9
b
±
c
a
(
2
a
)
2
b
2
a
2
(
2
a
)
2
2
a
Step 9
x
Step 10
b
±
4
a
2
c
a
4
a
2
b
2
4
a
2
2
a
Step 10
x
Step 11
b
±
4
a
2
b
2
4
a
2
2
a
Step 11
x
Step 12
b
±
4
a
c
b
2
2
a
Step 12
x
Step 13
b
±
b
2
4
a
c
Step 13
Complete the sentences.
 In Step 3, the missing expression is . 
 In Step 5, taking the square root of both sides gives . 
 In Step 11, simplifying the first term under the radical gives . 
 In Step 13, the expression  completes the quadratic formula. 
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