Question

Solve equations using factorization method:
$\frac{9}{2}x=5+x^2$

Answer 1

Step : Factorising the equation:

Given equation,

$\frac{9}{2}x=5+x^2$

$\Rightarrow 9x=10+2x^2$

$\Rightarrow 2x^2-9x+10=0$

$\Rightarrow 2x^2-5x-4x+10=0$

{factorizing left hand side}

$\Rightarrow x(2x-5)-2(2x-5)=0$

$\Rightarrow (2x-5)(x-2)=0$

$\Rightarrow 2x-5=0orx-2=0$

{zero product rule}

$\therefore x=\frac{5}{2}orx=2$

Hence, the required answer is

$x=\frac{5}{2}orx=2$.