Solving Absolute Value Equations
The equation in the next example involves absolute value.
Example 1
Solving an absolute value equation by factoring
Solve  x^{2}  2x  16
 = 8.
Solution
First write an equivalent compound equation without absolute value:
x^{2}  2x  16 = 8 
or 
x^{2}  2x  16 = 8 
x^{2}  2x  24 = 0 
or 
x^{2}  2x  8 = 0 
(x  6)(x + 4) = 0 
or 
(x  4)(x + 2) = 0 
x  6 = 0 
or 
x + 4 = 0 
or 
x  4 = 0 
or 
x + 2 = 0 
x = 6 
or 
x = 4 
or 
x = 4 
or 
x = 2 
The solution set is {2, 4, 4, 6}. Check each solution.
