Answer
$x=1\pm 7i$
Work Step by Step
Since $x^2=a$ implies $x=\pm\sqrt{a}$ (the Square Root Principle), the solutions to the given equation, $
(x-1)^2=-49
,$ are
\begin{array}{l}\require{cancel}
x-1=\pm\sqrt{-49}
\\\\
x-1=\pm\sqrt{-1}\cdot\sqrt{49}
\\\\
x-1=\pm i\cdot\sqrt{(7)^2}
\\\\
x-1=\pm i\cdot7
\\\\
x-1=\pm 7i
\\\\
x=1\pm 7i
.\end{array}