Solving the Equation x = y² for y

Unlock the depths of algebra as we solve the quadratic equation x = y². This equation frequently shows up in multiple fields such as physics, engineering, and even in economics. Understanding this equation will offer valuable insights into these disciplines.

Step 1: Starting Point

Math: x = y²

Explanation: We start off with our original equation. Here, we aim to isolate y in terms of x.

Step 2: Isolate y

Math: y² = x

Explanation: The equation is already simplified, and y² is isolated on one side.

Step 3: Solve for y

Math: y = √x or y = -√x

Explanation: To solve for y, we take the square root of both sides. However, we should remember that y can be either positive or negative.

Step 4: Final Equation

Math: y = ±√x

Explanation: This is our final expression for y in terms of x, covering both the positive and negative roots.

Conclusion

And there we have it! The equation x = y² can be re-arranged to yield y = ±√x. This simple yet effective transformation offers rich insights into the relationship between x and y, helping us solve real-world problems across different fields.