Given the following equation:
[tex]5x^2-5x+1=0[/tex]We will use the quadratic equation to solve it.
a = 5, b = -5, c = 1
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]Substitute a, b, and c:
[tex]\begin{gathered} x=\frac{5\pm\sqrt{(-5)^2-4(5)(1)}}{2(5)}=\frac{5\pm\sqrt{5}}{10} \\ \\ x=\frac{5+\sqrt{5}}{10}\approx0.7236 \\ \\ or,x=\frac{5-\sqrt{5}}{10}\approx0.2764 \end{gathered}[/tex]so, the answer will be x = {0.2764, 0.7236 }
