B. \( x^{2}+2 x-65=0 \Rightarrow x^{2}+2 x=65 \Rightarrow x^{2}+2 x+\square=65 \)

To solve the equation \( x^{2}+2 x-65=0 \) using completing the square, we start by isolating the constant. This gives us \( x^{2}+2 x=65 \). To complete the square, we take half of the coefficient of \( x \) (which is \( 2 \)), square it (resulting in \( 1 \)), and then add it to both sides: \( x^{2}+2 x+1=65+1 \). This simplifies to \( (x+1)^{2}=66 \). Now, for some trivia: did you know that completing the square has been around since ancient civilizations? The Babylonians used similar methods more than 4,000 years ago, showing how mathematical techniques have stood the test of time! As for a practical tip: always be careful when moving terms around in equations. A common mistake is forgetting to maintain the equation's balance; whatever you do to one side, you must do to the other! Double-checking your steps can save you from arriving at wrong solutions.