Fill in the blank with a number to make the expression a perfect square. \( x^{2}-18 x+\square \)

To make the expression \( x^{2}-18x+\square \) a perfect square, we need to find the value that completes the square. The coefficient of \( x \) is \(-18\), and we take half of that (-9) and square it, which gives us \( (-9)^{2} = 81 \). Thus, the expression becomes \( x^{2} - 18x + 81 \), which can be factored as \( (x - 9)^{2} \). The number to fill in the blank is \( 81 \). Now, let’s dive into some related fun tidbits! Completing the square is like magical algebra wizardry! This technique not only helps in identifying perfect squares but also plays a pivotal role in solving quadratic equations, making it a valuable tool in your math toolbox. Plus, it paves the path to understanding parabolas in coordinate geometry, helping visualize the beauty in mathematics! If you’re eager to explore more about this technique, dive into "Algebra and Trigonometry" by Michael Sullivan. It's packed with examples and practice problems that can turn you into a completing-the-square master! Who knows, you may even find yourself applying quadratic formulas in real-life scenarios, like determining the optimal dimensions of a garden for maximum area!