Question
Solve equation using factorisation method:
$\frac{9}{2} x=5+x^2$
$\frac{9}{2} x=5+x^2$
✓
Answer
$\frac{9}{2} x=5+x^2$
$\Rightarrow 9x = 10 + 2x^2$
$\Rightarrow 2x^2 - 9x + 10 = 0$
$\Rightarrow 2x^2 - 5x - 4x + 10 = 0$
$\Rightarrow x(2x - 5) - 2(2x -5) = 0$
$\Rightarrow (2x - 5) (x - 2) = 0$
since $2x - 5 = 0$ or $x - 2 = 0$
$\therefore 2x - 5 = 0$
$\therefore 2x = 5$
$\therefore x =\frac{5}{2}$
$\therefore x - 2 = 0$
$\therefore x = 2$
then $x=\frac{5}{2}$ or $x=2$
$\Rightarrow 9x = 10 + 2x^2$
$\Rightarrow 2x^2 - 9x + 10 = 0$
$\Rightarrow 2x^2 - 5x - 4x + 10 = 0$
$\Rightarrow x(2x - 5) - 2(2x -5) = 0$
$\Rightarrow (2x - 5) (x - 2) = 0$
since $2x - 5 = 0$ or $x - 2 = 0$
$\therefore 2x - 5 = 0$
$\therefore 2x = 5$
$\therefore x =\frac{5}{2}$
$\therefore x - 2 = 0$
$\therefore x = 2$
then $x=\frac{5}{2}$ or $x=2$
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