2 min read Jun 17, 2024

Solving the Equation (x^2 + 4)^2 = 0

This equation may seem a bit intimidating at first glance, but it's actually quite simple to solve. Let's break it down step by step:

Understanding the Equation

The equation (x² + 4)² = 0 represents a squared term being set equal to zero. This means that the expression inside the parentheses must also be equal to zero.

Solving for x

  1. Take the square root of both sides: √(x² + 4)² = √0
  2. Simplify: x² + 4 = 0
  3. Isolate x²: x² = -4
  4. Take the square root of both sides: x = ±√(-4)
  5. Simplify: x = ±2i (where 'i' is the imaginary unit, √-1)

The Solution

The solutions to the equation (x² + 4)² = 0 are x = 2i and x = -2i. These are complex numbers, as they involve the imaginary unit 'i'.

Key Takeaways

  • Squaring an expression sets it to zero only if the expression itself is zero.
  • The square root of a negative number results in an imaginary number.

This problem demonstrates the importance of understanding the properties of exponents and the concept of imaginary numbers when working with equations.