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CCGPS Geometry Worksheet: SOLVING QUADRATIC EQUATIONS
We have learned several different methods for solving quadratic equations. Below are examples of three
different methods that may come in handy.
Example #1: Solve by FACTORING.
x 2  6  7 x
Add 7x to both sides to get all terms to one side of equation = 0.
x2  7x  6  0
Factor. Since 1  6  6 and 1  6  7, we can factor the left hand side.
x  1x  6  0
Set each factor = 0.
x  1  0 or x  6  0
Solve for x.
x  1 or x  6
Example #2: Solve using the SQUARE ROOT PRINCIPAL.
x  32
5
Use the square root principal.
x  32
 5
Simplify.
x3  5
Solve for x by subtracting 3.
x  3  5
Example #3: Solve using the COMPLETING THE SQUARE.
x2  4x  5  0
x2  4x  5
Rewrite so all terms with “x” are on the left side.
x2  4x  4  5  4
Find the number that completes the square. Add it to both sides.
( x  2)2  9
Factor the perfect square trinomial. Simplify the right side.
( x  2)  3
Take the square root of both sides.
x  5,1
Solve for x.
Example #4: Solve using the QUADRATIC FORMULA.
 b  b 2  4ac
Given ax  bx  c  0 , the quadratic formula can give you the solution(s) for x. x 
2a
2
x 2  2 x  10
Add 7 to both sides to get all terms to one side of equation = 0.
x 2  2 x  10  0
Determine a, b and c. a = 1, b = –2, c = –10. Use quadratic formula.
x
x
  2 
 22  41 10
21
=
4  4   40 4  4  40 4  44


2
2
2
Simplify your answer.
4  44 4  2  2  11 4  2 11 4 2 11


 
 2  11 So the solutions are x  2  11 .
2
2
2
2
2
THE MORAL OF THE STORY:
Solve using the best method (if there is ( ) or no x term – use square roots
If there is an x term, move all terms to one side and try factoring
If you can’t factor and a is 1, complete the square
If you can’t factor and a is not 1, use the quadratic formula)
1. x 2  3x  4
6. 3x 2  7 x  2  0
2. x 2  10 x  25
7. x 2  3x  1  6
3. x 2  5  3
8. 4 x 2  7 x  2  0
4.
x  42
8
5. x 2  6 x  8  0
9. 8 x 2  200
10. x 2  6 x  1  0
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