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Mathematics

Solve the following equation by factorisation:

x(6x - 1) = 35

Quadratic Equations

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Answer

Given,

x(6x−1)=35⇒6x2−x−35=0 (Writing as ax2+bx+c=0)⇒6x2−15x+14x−35=0⇒3x(2x−5)+7(2x−5)=0⇒(3x+7)(2x−5)=0 (Factorising left side) ⇒3x+7=0 or 2x−5=0 (Zero-product rule) ⇒x=−73 or x=52x(6x - 1) = 35 \\[0.5em] \Rightarrow 6x^2 - x - 35 = 0 \text{ (Writing as } ax^2 + bx + c = 0) \\[0.5em] \Rightarrow 6x^2 - 15x + 14x - 35 = 0 \\[0.5em] \Rightarrow 3x(2x - 5) + 7(2x - 5) = 0 \\[0.5em] \Rightarrow (3x + 7)(2x - 5) = 0 \text{ (Factorising left side) } \\[0.5em] \Rightarrow 3x + 7 = 0 \text{ or } 2x - 5 = 0 \text{ (Zero-product rule) }\\[0.5em] \Rightarrow x = -\dfrac{7}{3} \text{ or } x = \dfrac{5}{2}

Hence, the roots of given equation are −73-\dfrac{7}{3}, 52\dfrac{5}{2}.

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