Question
Solve equation by factorisation : $x(x + 1) + (x + 2)(x + 3) = 42$
✓
Answer
$x(x + 1) + (x + 2)(x + 3) = 42$
$\Rightarrow 2x^2 + 6x + 6 – 42 = 0$
$\Rightarrow x2 + 3x – 18 = 0$
$\Rightarrow x^2+ 3x – 18 = 0 ..$(Dividing by $2)$
$\Rightarrow x^2 + 6x – 3x – 18 = 0$
$\Rightarrow x(x + 6) 3(x + 6) = 0$
$\Rightarrow (x + 6)(x – 3) = 0$
Either $x+6=0$,
then $x = –6$
or
$x-3=0$
then $x=3$
Hence $x=-6,3$.
$\Rightarrow 2x^2 + 6x + 6 – 42 = 0$
$\Rightarrow x2 + 3x – 18 = 0$
$\Rightarrow x^2+ 3x – 18 = 0 ..$(Dividing by $2)$
$\Rightarrow x^2 + 6x – 3x – 18 = 0$
$\Rightarrow x(x + 6) 3(x + 6) = 0$
$\Rightarrow (x + 6)(x – 3) = 0$
Either $x+6=0$,
then $x = –6$
or
$x-3=0$
then $x=3$
Hence $x=-6,3$.
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