# Solve the quadratic equation by factorization a^2b^2x^2+b^2x-a^2x-1=0

Solve the quadratic equation by factorization
${a}^{2}{b}^{2}{x}^{2}+{b}^{2}x-{a}^{2}x-1=0$
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Step 1
Given
${a}^{2}{b}^{2}{x}^{2}+{b}^{2}x-{a}^{2}x-1=0$
Step 2 Solving
$\left({a}^{2}{b}^{2}{x}^{2}+{b}^{2}x\right)-\left({a}^{2}x-1\right)=0$
$\left({a}^{2}x+1\right){b}^{2}x-\left({a}^{2}x+1\right)=0$
$\left({a}^{2}x+1\right)\left({b}^{2}x-1\right)=0$
${a}^{2}x+1=0,{b}^{2}x-1=0$
${a}^{2}x=-1,{b}^{2}x=1$
$x=\frac{-1}{{a}^{2}},x=\frac{1}{{b}^{2}}$
$\therefore x=\frac{-1}{{a}^{2}},\frac{1}{{b}^{2}}$