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Question
Solve the following equation by factorization
`(1)/(7)(3x – 5)^2`= 28
Solution
`(1)/(7)(3x – 5)^2`= 28
(3x – 5)2 = 28 × 7
⇒ 9x2 – 30x + 25 = 196
⇒ 9x2 - 30x + 25 - 196 = 0
⇒ 9x2 - 30x - 171 = 0
⇒ 3x2 - 10x - 57 = 0
⇒ 3x2 - 19x + 9x - 57 = 0
⇒ x(3x - 19) + 3 (3x - 19) = 0
⇒ (3x - 19) (x + 3) = 0
Either 3x - 19 = 0,
then 3x = 19
⇒ x = `(19)/(3)`
or
x + 3 = 0,
then x = -3
Hence x = `(19)/(3)`, -3.
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