Question

Solve the equation 2x²-5x+3=0 , by the method of completing square

Answer 1

$$\begin{gathered} \mathrm{The}\mathrm{given}\mathrm{equation}\mathrm{is}: \\ 2x^2-5x+3=0 \\ \Rightarrow x^2-\frac{5}{2}x+\frac{3}{2}x=0\left[\mathbf{dividing}\mathbf{}\mathbf{both}\mathbf{}\mathbf{sides}\mathbf{}\mathbf{by}\mathbf{}\mathbf{2}\right] \\ \Rightarrow x^2-\frac{5}{2}x+\frac{25}{16}+\frac{3}{2}-\frac{25}{16}=0 \\ \Rightarrow {\left(x-\frac{5}{4}\right)}^2=\frac{25}{16}-\frac{3}{2} \\ \Rightarrow {\left(x-\frac{5}{4}\right)}^2=\frac{25-24}{16} \\ \Rightarrow {\left(x-\frac{5}{4}\right)}^2=\frac{1}{16} \\ \Rightarrow x-\frac{5}{4}=\pm \frac{1}{4} \\ \Rightarrow x=\frac{5}{4}\pm \frac{1}{4} \\ \Rightarrow x=\frac{5}{4}+\frac{1}{4}\mathrm{or}x=\frac{5}{4}-\frac{1}{4} \\ \Rightarrow x=\frac{6}{4}\mathrm{or}x=\frac{4}{4} \\ \Rightarrow x=\frac{3}{2}\mathrm{or}x=1 \end{gathered}$$