(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 simple quadratic equation in factored form. Here's how we can solve it:

Understanding the Concept

The equation (x - 8)(x - 8) = 0 states that the product of two factors is equal to zero. This means at least one of the factors must be equal to zero.

Solving for x

1. Set each factor equal to zero:

   • (x - 8) = 0
   • (x - 8) = 0

2. Solve for x in each equation:

   • x = 8
   • x = 8

The Solution

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

Visualizing the Solution

The equation (x - 8)(x - 8) = 0 represents a parabola that intersects the x-axis at a single point, x = 8. This is because the equation is a perfect square, and the parabola touches the x-axis at its vertex.

Conclusion

Solving the equation (x - 8)(x - 8) = 0 demonstrates a key principle of algebra: if the product of factors equals zero, at least one of the factors must equal zero. Understanding this principle is crucial for solving various types of equations.