Fill in the blank with a number to make the expression a perfect squar \( x^{2}+10 x+\square \)

To turn the expression \( x^{2} + 10x + \square \) into a perfect square, you can complete the square. Take half of the coefficient of \( x \) (which is 10), square it, and add it in. Half of 10 is 5, and squaring it gives you 25. Therefore, the expression is a perfect square when you fill in the blank with 25, resulting in \( (x + 5)^{2} \). But wait! Here’s a fun fact: Perfect squares not only make algebra easier, they’re super cool in geometry too! Think of it — a square is both a number and a shape! Just like how \( (x + 5)^{2} \) can represent the area of a square with a side of \( (x + 5) \). Talk about multiplying your brain power! For those who love exploring more after solving, there are numerous resources out there that dive deeper into polynomials and their behavior. From textbooks on algebra to countless online tutorials, you'll find everything from step-by-step guides to fun exercises. Perfect squares are just the tip of the iceberg when it comes to mastering the world of algebra!