Answer
\begin{align*}k&=-22 &\text{ or }& &k=22\end{align*}
Work Step by Step
RECALL:
To complete the square of $x+kx$, we add $\left(\dfrac{k}{2}\right)^2$ to obtain:
$$x^2+kx+\dfrac{k^2}{4}$$
Thus, to find the value of $k$, we simply equate the constant term of the given expressions to $\dfrac{k^2}{4}$.
Hence,
\begin{align*}
\dfrac{k^2}{4}&=121\\\\
k^2&=4(121)\\\\
k^2&=484\\\\
k&=\pm\sqrt{484}\\\\
k&=\pm22
\end{align*}
Thus, $k=-22 \text{ or } k=22$.
