Answer
$x=1-4i,1+4i$
Work Step by Step
Plug the values $a$, $b$, and $c$ into the quadratic formula and simplify all the values.
$x^2-2x+17=0$
$a=1,b=-2,c=17$
$x=\frac{-b±\sqrt {b^2-4ac}}{2a}$
$x=\frac{-(-2)±\sqrt {(-2)^2-4(1)(17)}}{2(1)}$
$x=\frac{2±\sqrt {4-68}}{2}$
$x=\frac{2±\sqrt {-64}}{2}$
$x=\frac{2±8i}{2}$
$x=1±4i$
$x=1-4i,1+4i$