(x+8)(x+8)=0

Jasonbradley

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Jun 17, 2024

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Solving the Equation (x+8)(x+8) = 0

This equation represents a quadratic equation in its factored form. Let's break down how to solve for the value of 'x'.

Understanding the Equation

• Factored form: The equation is already factored. This means it's written as a product of two expressions: (x+8) and (x+8).
• Zero Product Property: The Zero Product Property states that if the product of two or more factors is zero, then at least one of the factors must be zero.

Solving for 'x'

1. Apply the Zero Product Property: Since the product of (x+8) and (x+8) is zero, we know that at least one of these factors must be zero.
2. Set each factor equal to zero:
   • (x+8) = 0
   • (x+8) = 0
3. Solve for 'x' in each equation:
   • x = -8
   • x = -8

Solution

The solution to the equation (x+8)(x+8) = 0 is x = -8. This is a double root, meaning the solution appears twice.

Graphical Interpretation

The equation represents a parabola that touches the x-axis at the point (-8, 0). The fact that it's a double root means the parabola touches the x-axis but doesn't cross it.