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Question
Solve the following equation by factorization
(x – 4)2 + 52 = 132
Solution
(x – 4)2 + 52 = 132
x2 – 8x + 16 + 25 = 169
x2 - 8x + 41 - 169 = 0
⇒ x2 - 8x - 128 = 0
⇒ x2 - 16x + 8x - 128 = 0
⇒ x (x - 16) + 8(x - 16) = 0
⇒ (x - 16) (x + 8) = 0
Either x - 16 = 0,
then x = 16
or
x + 8 = 0,
then x = -8
Hence x = 16, -8.
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