Question

Find the root of the following quadratic equation, if they exist , by the method of completing the square:
$2x^2-7x+3=0$

Answer 1

$\begin{array}{c}Assumingx=aand\frac{7}{4}=b,theL.H.Sofequationismadeintheformof{\left(a-b\right)}^2\\ \Rightarrow {\left(x-\frac{7}{4}\right)}^2=\frac{49}{16}-\frac{3}{2}\\ \Rightarrow {\left(x-\frac{7}{4}\right)}^2=\frac{49-24}{16}\\ \Rightarrow {\left(x-\frac{7}{4}\right)}^2=\frac{25}{16}\\ case1:\\ \Rightarrow x-\frac{7}{4}=\frac{5}{4}\\ \Rightarrow x=\frac{7}{4}+\frac{5}{4}=\frac{12}{4}=3\\ case2:\\ \Rightarrow x-\frac{7}{4}=-\frac{5}{4}\\ \Rightarrow x=\frac{7}{4}+\frac{-5}{4}=\frac{2}{4}=\frac{1}{2}\\ Hence,x=3andx=\frac{1}{2}\end{array}$