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Question
Solve equation using factorisation method:
4(2x – 3)2 – (2x – 3) – 14 = 0
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Solution
4(2x – 3)2 – (2x – 3) – 14 = 0
Let 2x – 3 = y
Then 4y2 – y – 14 = 0
⇒ 4y2 – 8y + 7y – 14 = 0
⇒ 4y(y – 2) + 7(y – 2) = 0
⇒ (y – 2)(4y + 7) = 0
If y – 2 = 0 or 4y + 7 = 0
⇒ y = 2 or y = `(-7)/4`
⇒ 2x – 3 = 2 or 2x – 3 = `(-7)/4`
⇒ 2x = 5 or 2x = `5/4`
⇒ x = `5/2` or x = `5/8`
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