Question

Find the roots of the following quadratic equations by the method of completing the square: $2x^2+x-4=0$

Answer 1

$\therefore 2x^2+x-4=0$

using method of compleating of square

$\Rightarrow 2x^2+x+\frac{1}{8}-\frac{1}{8}-4=0$

$\Rightarrow (\sqrt{2}x+\frac{1}{2\sqrt{2}}{)}^2-\frac{33}{8}=0$

$(\sqrt{2}x+\frac{1}{2\sqrt{2}}{)}^2-(\sqrt{\frac{33}{8}}{)}^2=0$

$\Rightarrow [\sqrt{2}x+\frac{1}{2\sqrt{2}}-\sqrt{\frac{33}{8}}][\sqrt{2}x+\frac{1}{2\sqrt{2}}+\sqrt{\frac{33}{8}}]=0$

$\Rightarrow x=\frac{1}{8}[1-\sqrt{33}]\&\frac{-1}{8}[1+\sqrt{33}]$