Download Worksheet: Section 2

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
x2  7x  6  0
Add 7x to both sides to get all terms to one side of equation = 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
Simplify.
 5
x3  5
Solve for x by subtracting 3.
x  3  5
Example #3: Solve using the QUADRATIC FORMULA.
Given ax 2  bx  c  0 , the quadratic formula can give you the solution(s) for x. x 
 b  b 2  4ac
2a
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
Try the factoring method or solving by the square root principal first.
If all else fails… use the Quadratic Formula.
SOLVE for x.
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. 2 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. 4 x 2  6 x  1  0
11. The length of a rectangle is 2 feet more than its width. Find the dimensions of the rectangle if its area
is 63 square feet.