When dealing with algebraic equations, determining the inverse equation can be a challenging task. In this article, we will explore how to find the inverse equation of the equation 2(x – 2)^2 = 8(7 + y). By following a systematic approach and understanding the steps involved, we can unravel the mystery of finding the inverse equation.
Solving for y: Finding the Inverse Equation
To find the inverse equation of 2(x – 2)^2 = 8(7 + y), our first step is to isolate the variable y. We begin by expanding the terms on both sides of the equation to simplify the expression. This results in 2(x^2 – 4x + 4) = 56 + 8y. Next, we distribute the 2 on the left side to get 2x^2 – 8x + 8 = 56 + 8y. By rearranging the terms, we can isolate the variable y, leading to 8y = 2x^2 – 8x – 48. Finally, to find the inverse equation, we divide by 8 to obtain y = 1/4x^2 – x – 6.
Understanding the Steps to Determine the Inverse Equation
It is essential to understand the steps involved in determining the inverse equation of a given equation. By following a systematic approach and applying algebraic principles, we can simplify the equation to isolate the variable y. In this case, expanding and simplifying the equation, then rearranging the terms to isolate y, allows us to find the inverse equation. This process requires attention to detail and a solid understanding of algebraic concepts.
In conclusion, finding the inverse equation of 2(x – 2)^2 = 8(7 + y) requires patience and a methodical approach. By following the steps outlined above and understanding the principles of algebra, we can unravel the mystery of determining the inverse equation. It is important to practice solving similar equations to build confidence and proficiency in algebraic manipulation. The ability to find the inverse equation of a given equation is a valuable skill that can be applied to various mathematical problems and real-world scenarios.