Download Quadratic Equations: Solve by factoring

Quadratic Equation: Solving by factoring
Example: Solve 6x2 – 13x = 8.
First get all nonzero terms
6x2 – 13x – 8
on one side.
Second factor completely. 6x2 – 16x + 3x – 8
2x(3x – 8) + 1(3x – 8)
(3x – 8)(2x + 1)
Third, set each factor
equal to zero.
Last, solve each linear
equation.
= 0
= 0
= 0
= 0
3x – 8 = 0 or 2x + 1 = 0
3x = 8 or 2x = - 1
8
1
x  or x  
3
2
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Quadratic Equation: Solving by factoring
Try to solve
12x2
1 

= 27x – 6. The solution set is  , 2 .
4 
Notes: Solving 12x2 = 27x – 6 resulted in three factors;
3, 4x – 1, and x – 2. Setting the factor 3 equal to zero
results in a contradiction, so it does not contribute a
number to the solution set.
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Quadratic Equation: Solving by factoring
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