A Clever Trick for a Complex Equation

Can you solve this interesting algebra problem? At first glance, this looks like a complicated fourth-degree equation that would be a nightmare to expand. However, if you look closely at the two expressions (x^2 + 6x + 1) and (x^2 + 6x - 3), you'll notice a repeating pattern. In this video, we use a clever substitution (u = x^2 + 6x) to transform this intimidating problem into a simple quadratic equation. From there, we factor, solve for u, and then substitute back to find all four real solutions for x. We’ll walk through: Identifying the repeating expression for substitution. Solving the resulting quadratic equation by factoring. Using the completing the square method to find the final values of x. Did you use a different method, like the quadratic formula, to solve this? Let me know your thoughts and solutions in the comments below! If you enjoyed this math challenge, don't forget to like the video and subscribe to Logic Booster for more daily logic puzzles and mathematical insights!