(x^2+8)(x^2-8)=0

Jasonbradley

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Jun 17, 2024

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Solving the Equation: (x^2 + 8)(x^2 - 8) = 0

This equation presents a straightforward approach to solving for the unknown variable 'x'. The key lies in understanding the Zero Product Property. This property states that if the product of two or more factors is zero, then at least one of the factors must be zero.

Let's apply this to our equation:

(x^2 + 8)(x^2 - 8) = 0

We have two factors: (x^2 + 8) and (x^2 - 8). To make the product equal to zero, at least one of these factors must be equal to zero.

Therefore, we set each factor equal to zero and solve:

1. x^2 + 8 = 0

• Subtract 8 from both sides:
  • x^2 = -8
• Take the square root of both sides:
  • x = ±√(-8)
• Simplify:
  • x = ±2√(-2)
• Express in terms of imaginary unit 'i' (where i² = -1):
  • x = ±2i√2

2. x^2 - 8 = 0

• Add 8 to both sides:
  • x^2 = 8
• Take the square root of both sides:
  • x = ±√8
• Simplify:
  • x = ±2√2

Therefore, the solutions to the equation (x^2 + 8)(x^2 - 8) = 0 are:

• x = 2√2
• x = -2√2
• x = 2i√2
• x = -2i√2