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Question
Solve equation using factorisation method:
`9/2 x = 5 + x^2`
Solution
`9/2 x = 5 + x^2`
⇒ 9x = 10 + 2x2
⇒ 2x2 – 9x + 10 = 0
⇒ 2x2 – 5x – 4x + 10 = 0
⇒ x(2x – 5) – 2(2x – 5) = 0
⇒ (2x – 5)(x – 2) = 0
Since 2x – 5 = 0 or x – 2 = 0
∴ 2x – 5 = 0
∴ 2x = 5
∴ x = `5/2`
∴ x – 2 = 0
∴ x = 2
Then x = `5/2` or x = 2
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