Solving Equations Examples And Worksheet Page 6
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14A54
Appendix A
Review of Fundamental Concepts of Algebra
2
When solving quadratic equations by completing the square, you must add
b 2
to each side in order to maintain equality. If the leading coefficient is not 1, you must
divide each side of the equation by the leading coefficient before completing the square,
as shown in Example 7.
Example 6
Completing the Square: Leading Coefficient Is 1
2
Solve
x
2x
6
0
by completing the square.
Solution
2
x
2x
6
0
Write original equation.
2
x
2x
6
Add 6 to each side.
2
2
2
x
2x
1
6
1
2
Add
1
to each side.
2
half of 2
2
x
1
7
Simplify.
±
x
1
7
Take square root of each side.
±
x
1
7
Subtract 1 from each side.
±
The solutions are
x
1
7.
Check these in the original equation.
Now try Exercise 73.
Example 7
Completing the Square: Leading Coefficient Is Not 1
2
3x
4x
5
0
Original equation
2
3x
4x
5
Add 5 to each side.
4
5
2
x
x
Divide each side by 3.
3
3
2
2
4
2
5
2
2
2
2
x
x
Add
to each side.
3
3
3
3
3
2
4
half of
3
4
4
19
2
x
x
Simplify.
3
9
9
2
2
19
x
Perfect square trinomial
3
9
2
19
±
x
Extract square roots.
3
3
2
19
±
x
Solutions
3
3
Now try Exercise 77.
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