Chapter 4 - Quadratic Functions and Equations - 4-6 Complete the Square - Practice and Problem-Solving Exercises - Page 238: 58

$k=10$

Recall: $a^2+2ab+b^2=(a+b)^2$ Find $a$ by taking the principal square root of the first term to obain: $\sqrt{25x^2}=5x$ Find $b$ by taking the principal square root of the last term to obtain: $b=\sqrt{1}=1$ Thus, the middle term of the given trinomial is: $=2(5x)(1)\\ =10x$ Thus, $k=10$.