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Question
Solve the following equation by factorization
`(2)/(3)x^2 - (1)/(3)x` = 1
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Solution
`(2)/(3)x^2 - (1)/(3)x` = 1
⇒ 2x2 - x = 3
⇒ 2x2 - x - 3 = 0
⇒ 2x2 - 3x + 2x - 3 = 0
⇒ x(2x - 3) + 1(2x - 3) = 0
⇒ (2x - 3) (x + 1) = 0
Either 2x - 3 = 0,
then 2x = 3
⇒ x = `(3)/(2)`
or
x + 1 = 0,
then x = -1
Hence x = `(3)/(2)`, -1.
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