Solve (9/2)x = 5 + x^2 by factorisation

Mathematics

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Given,

⇒ $\dfrac{9}{2}x = 5 + x^2$

⇒ 9x = 2(5 + x²)

⇒ 9x = 10 + 2x²

⇒ 2x² - 9x + 10 = 0

⇒ 2x² - 4x - 5x + 10 = 0

⇒ 2x(x - 2) - 5(x - 2) = 0

⇒ (2x - 5)(x - 2) = 0

⇒ 2x - 5 = 0 or x - 2 = 0 [Using Zero-product rule]

⇒ 2x = 5 or x = 2

⇒ x = $\dfrac{5}{2}$ or x = 2.

Hence, x = 2 or x = $\dfrac{5}{2}$ .

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