Answer
$$7 \pm 2 j .$$
Work Step by Step
For the equation $x^2 - 14x + 53= 0$, we use the quadratic formula as follows
$$ x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}, \\a=1, \quad b=-14, \quad c=53 .$$ That is, $$ x=\frac{14 \pm \sqrt{(-14)^2-4(53)}}{2 }=\frac{14 \pm 4j}{2 }= 7 \pm 2 j .$$
