Question

Solve equations using factorization method:

$(x+1)(2x+8)=(x+7)(x+3)$

Answer 1

Step: Factorising the equation:

$(x+1)(2x+8)=(x+7)(x+3)$

$\Rightarrow 2x^2+2x+8x+8=x^2+7x+3x+21$

$\Rightarrow x^2-13=0$

$\Rightarrow x^2-(\sqrt{13}{)}^2=0$

$\Rightarrow (x-\sqrt{13})(x+\sqrt{13})=0$

$\left[\because (a^2-b^2)=(a-b)(a+b)\right]$

$\Rightarrow x-\sqrt{13}=0orx+\sqrt{13}=0$

{zero product rule}

$\therefore x=\sqrt{13}orx=-\sqrt{13}$

Hence, the required answer is $x=\sqrt{13}orx=-\sqrt{13}$.