Solve 5x 2 - 7x + 2 = 0 by completing the square. What are the solutions?

Answer:[tex]x=\frac{2}{5}[/tex] or [tex]x=1[/tex] Step-by-step explanation:The given quadratic equation is[tex]5x^2-7x+2=0[/tex]Group the constant terms on the right hand side.[tex]5x^2-7x=0-2[/tex][tex]5x^2-7x=-2[/tex]Divide through by 5.[tex]x^2-\frac{7}{5}x=-\frac{2}{5}[/tex]Add the square of half the coefficient of x., which is [tex](\frac{1}{2}\times- \frac{7}{5})^2=\frac{49}{100}[/tex] to both sides of the equation.[tex]x^2-\frac{7}{5}x+\frac{49}{100}=-\frac{2}{5}+\frac{49}{100}[/tex]The left hand side is now a perfect square.[tex](x-\frac{7}{10})^2=\frac{9}{100}[/tex]Take the square root of both sides;[tex](x-\frac{7}{10})=\pm \sqrt{\frac{9}{100}}[/tex][tex]x-\frac{7}{10}=\pm \frac{3}{10}[/tex][tex]x=\frac{7}{10}\pm \frac{3}{10}[/tex][tex]x=\frac{7-3}{10}[/tex] or [tex]x=\frac{7+3}{10}[/tex][tex]x=\frac{4}{10}[/tex] or [tex]x=\frac{10}{10}[/tex][tex]x=1[/tex] or [tex]x=\frac{2}{5}[/tex]