Answer
\begin{align*}
k&=-10 &\text{and}& &k=10
\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}&=25\\\\
k^2&=4(25)\\\\
k^2&=100\\\\
k&=\pm\sqrt{100}\\\\
k&=\pm10
\end{align*}
Thus, $k=-10 \text{ or } k=10$.