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SOLVING SIMPLE QUADRATIC EQUATIONS BY FACTORING

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To solve a quadratic equation by factoring: 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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