The expression ‘2x2 + 8x + x2 = 16′ represents a quadratic equation. The task involves finding the value of ‘x’ that satisfies this equation. Simplifying the equation leads to a standard quadratic form which can then be solved using various methods such as factoring, completing the square, or applying the quadratic formula. In this instance, combining like terms results in 3x2 + 8x = 16 or 3x2 + 8x – 16 = 0.
Solving quadratic equations is a fundamental skill in algebra and has applications in various fields, including physics, engineering, and economics. Understanding how to determine the roots of a quadratic equation is essential for modeling and solving real-world problems. The process of finding the root provides insights into the behavior of the quadratic function and the nature of its solutions. Historically, quadratic equations have been studied for centuries, with methods for their solution dating back to ancient civilizations.