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SOLVING SIMPLE QUADRATIC EQUATIONS BY FACTORING
Jump right to the exercises!
To solve a quadratic equation by factoring:
- put it in standard form, ax2 + bx + c = 0
- factor the left-hand side
- use the Zero Factor Law
EXAMPLE:
Solve: x2 = 2 - x
Solution:
Write a nice, clean list of equivalent equations:
|
x2 = 2 - x |
(original equation) |
|
x2 + x - 2 = 0 |
(put in standard form: subtract 2 from both sides; add x to both sides) |
|
(x + 2)(x - 1) = 0 |
(factor the left-hand side) |
|
x + 2 = 0 or x - 1 = 0 |
(use the Zero Factor Law) |
|
x = -2 or x = 1 |
(solve the simpler equations) |
MORE EXAMPLES:
Solve: (x + 3)(x - 2) = 0
Note: Don't multiply it out, if it's already in factored form, with zero on one side!
x + 3 = 0 or x - 2 = 0
x = -3 or x = 2
Solve: (2x - 3)(1 - 3x) = 0
2x - 3 = 0 or 1 - 3x = 0
2x = 3 or 1 = 3x
x = 3/2 or x = 1/3
Solve: x2 + 4x - 5 = 0
(x + 5)(x - 1) = 0
x + 5 = 0 or x - 1 = 0
x = -5 or x = 1
Solve: x2 = 5x + 14
x2 - 5x - 14 = 0
(x - 7)(x + 2) = 0
x - 7 = 0 or x + 2 = 0
x = 7 or x = -2
Solve: 6x = 2x2
3x = x2
x2 - 3x = 0
x(x - 3) = 0
x = 0 or x - 3 = 0
x = 0 or x = 3
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