Chapter 1 - Section 1.3 - Complex Numbers; Quadratic Equations in the Complex Number System - 1.3 Assess Your Understanding - Page 112: 65

$\displaystyle \frac{1}{5}\pm\frac{2}{5}i$

$5x^{2}+1=2x$ $5x^{2}-2x+1=0$ We solve using the quadratic formula ($a=5,\ b=-2,\ c=1$): $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ $x=\frac{-(-2)\pm\sqrt{(-2)^{2}-4(5)(1)}}{2(5)}$ $x=\frac{-(-2)\pm\sqrt{4-20}}{2(5)}$ $x=\frac{+2\pm\sqrt{-16}}{10}$ $x=\frac{2\pm 4i}{10}=\frac{1}{5}\pm\frac{2}{5}i$ Recall, $i=\sqrt{-1}$