Quadratic Equations Worksheet Page 4
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816.2 Completing The Square
The idea behind the completing the square method is to modify an equation that is otherwise
unfactorable so that the square root principle can be used. Here are the steps to follow for
completing the square:
+
−
=
2
Sample Problem:: Solve the equation
x
10
x
3
0
≠
2
Step 1:
If
a
1
, first divide the equation by a (the number in front of
x ).
+
−
=
2
x
10
x
3
0
Step 2:
Move the constant term to one side. Get the variables alone on one side.
(Note: In this
method, we do NOT put the equation in standard form)
+
=
2
x
10
x
3
Step 3:
We now divide b by 2, square this, and add this to both sides. This will “complete the
2
⎛
⎞
10
=
square”, hence the name. Since
⎜
⎟
, we add this to both sides.
25
⎝
⎠
2
+
+
=
+
2
x
10
x
25
3
25
or
+
+
=
2
x
10
x
25
28
Step 4:
Factor the side with the quadratic term. Note that this will always factor into a perfect
square.
+
+
=
(
x
5
)(
x
) 5
28
or
+
=
2
(
x
) 5
28
Step 5:
Use the square root property to solve the equation.
+
=
2
(
x
) 5
28
+
5 ±
=
x
28
=
−
5 ±
x
28
=
−
5 ±
x
2
7
=
−
+
=
−
−
The solutions are
x
5
2
, 7
x
5
2
7
.
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