Question
Solve equation using factorisation method:
$4(2x - 3)^2 - (2x - 3) - 14 = 0$
$4(2x - 3)^2 - (2x - 3) - 14 = 0$
✓
Answer
$4(2 x-3)^2-(2 x-3)-14=0$
$\text { Let } 2 x-3=y$
$\text { then } 4 y^2-y-14=0$
$\Rightarrow 4 y 2-8 y+7 y-14=0$
$\Rightarrow 4 y(y-2)+7(y-2)=0$
$\Rightarrow(y-2)(4 y+7)=0$
$\text { If } y-2=0 \text { or } 4 y+7=0$
$\Rightarrow y=2 \text { or } y=\frac{-7}{4}$
$\Rightarrow 2 x-3=2 \text { or } 2 x-3=\frac{-7}{4}$
$\Rightarrow 2 x=5 \text { or } 2 x=\frac{5}{4}$
$\Rightarrow x=\frac{2}{5} \text { or } x =\frac{5}{8}$
$\text { Let } 2 x-3=y$
$\text { then } 4 y^2-y-14=0$
$\Rightarrow 4 y 2-8 y+7 y-14=0$
$\Rightarrow 4 y(y-2)+7(y-2)=0$
$\Rightarrow(y-2)(4 y+7)=0$
$\text { If } y-2=0 \text { or } 4 y+7=0$
$\Rightarrow y=2 \text { or } y=\frac{-7}{4}$
$\Rightarrow 2 x-3=2 \text { or } 2 x-3=\frac{-7}{4}$
$\Rightarrow 2 x=5 \text { or } 2 x=\frac{5}{4}$
$\Rightarrow x=\frac{2}{5} \text { or } x =\frac{5}{8}$
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