Download Quadratics Test Review

Worksheet: SOLVING QUADRATIC EQUATIONS
Math 90
We have learned several different methods for solving quadratic equations. Below are examples of
two 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 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
THE MORAL OF THE STORY:
Try the factoring method first.
If all else fails… use the Quadratic Formula.
SOLVE for x.
1. x 2 − 3 x = 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. 4 x 2 − 6 x − 1 = 0
Algebra Review Solving Quadratics
____________________
Name
PROBLEM SOLVING
I.
Solve by Factoring
1.) x2 – 64 = 0
2.) x2 – 6x – 16 = 0
3.) x2 + 3x = 40
4.) 2 x 2 + 3x + 1 = 0
5.)
6.)
III. Solve by using the quadratic formula:
The quadratic formula is:
x=
7.
4x² – 8x = 1
9.
x² + 3x + 2 = 0
8.
x² – 100 = 0
Solve each equation any way you want. Show your work.
10. x2 + 11x + 18 = 0
11. x2 + 2x + 1 = 15
13.
(x + 2)² = 36
16.
x² = 36
14.
17.
x² – 10x + 25 = 0
x² – 6x + 2 = 0
x² + 6x = 0
x² + 8x = 0
12. 7x2 – 9x +1 = 0
15.
18. x² – 5x + 4 = 0
x² + 3x + 7 = 0
REASONING:
20.) Explain why x² = -81 DOES NOT have a solution.
Explain why:
24.) What are the two mistakes in setting up the quadratic formula:
Solve: 2x² – x – 6 = 0
− 1 ± (−1) 2 − 4(2)(6)
x=
2(2)