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Question
Use the substitution y = 2x + 3 to solve for x, if 4(2x + 3)2 – (2x + 3) – 14 = 0.
Solution
4(2x + 3)2 – (2x + 3) – 14 = 0
Put 2x + 3 = y
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
Then 2x + 3 – 2 = 0 or 4(2x + 3) + 7 = 0
⇒ 2x = –1 or 8x = –19
⇒ x = `(-1)/2` or x = `(-19)/8`
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