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Solving Absolute Value Equations

The equation in the next example involves absolute value.

Example 1

Solving an absolute value equation by factoring

Solve | x² - 2x - 16 | = 8.

Solution

First write an equivalent compound equation without absolute value:

x² - 2x - 16 = 8			or	x² - 2x - 16 = -8
x² - 2x - 24 = 0			or	x² - 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.