Question

Solve the following by using the method of completing square.
$5x^2-4x-10=0$

Answer 1

Given,

$\begin{array}{c}5x^2-4x-10=0\\ \Rightarrow 5\left[x^2-\frac{4}{5}x+{\left(\frac{2}{5}\right)}^2-{\left(\frac{2}{5}\right)}^2\right]-10=0\\ \Rightarrow 5{\left(x-\frac{2}{5}\right)}^2-\frac{4}{5}-10=0\\ \Rightarrow {\left(x-\frac{2}{5}\right)}^2=\frac{54}{25}\\ x-\frac{2}{5}=\pm \frac{\sqrt{54}}{25}\\ x=\frac{2-\sqrt{54}}{5}or\frac{2+\sqrt{54}}{5}\end{array}$