Answer
$\{1-3i\sqrt 2,1+3i\sqrt 2\}$
Work Step by Step
We have to solve the equation:
$$x^2-2x+19=0.$$
The equation is in the standard form.
To solve the equation $ax^2+bx+c=0$ we will use the quadratic formula:
$$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$$
Identify $a$, $b$, $c$:
$$\begin{align*}
a&=1\\
b&=-2\\
c&=19.
\end{align*}$$
We solve the given equation by substituting the values of $a$, $b$, $c$ in the quadratic formula:
$$\begin{align*}
x&=\dfrac{-(-2)\pm\sqrt{(-2)^2-4(1)(19)}}{2(1)}\\
&=\dfrac{2\pm\sqrt{-72}}{2}\\
&=\dfrac{2\pm 6\sqrt 2i}{2}\\
&=1\pm3i\sqrt 2.
\end{align*}$$
The solution set of the equation is:
$$\{1-3i\sqrt 2,1+3i\sqrt 2\}.$$