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Question
Solve the following quadratic equation by completing the square method
`(5x + 7)/(x - 1)` = 3x + 2
Solution
(3x + 2) (x – 1) = 5x + 7
3x2 – 3x + 2x – 2 = 5x + 7
⇒ 3x2 – x – 5x – 2 – 7 = 0
3x2 – 6x – 9 = 0
⇒ x2 – 2x – 3 = 0 ....(divided by 3)
x2 – 2x = 3
Adding `(1/2 xx 2)^2` on both sides
x2 – 2x + 1 = 3 + 1
(x – 1)2 = 4
⇒ x – 1 = `sqrt(4)`
x – 1 = ± 2
x – 1 = 2 or x – 1 = – 2
x = 3 or x = – 1
The solution set is – 1 and 3
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