(x+1)(x-8)=0

Jasonbradley

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Jun 16, 2024

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Solving the Equation (x+1)(x-8)=0

This equation represents a quadratic equation in factored form. To solve it, we can utilize the Zero Product Property, which states that if the product of two or more factors is zero, then at least one of the factors must be zero.

Applying the Zero Product Property

1. Set each factor equal to zero:

   • x + 1 = 0
   • x - 8 = 0

2. Solve for x in each equation:

   • x = -1
   • x = 8

Solution

Therefore, the solutions to the equation (x+1)(x-8)=0 are x = -1 and x = 8.

Interpretation

These solutions represent the x-intercepts of the parabola represented by the quadratic equation. The parabola intersects the x-axis at the points (-1, 0) and (8, 0).

Verification

We can verify our solutions by substituting them back into the original equation:

• For x = -1:

  • (-1 + 1)(-1 - 8) = (0)(-9) = 0

• For x = 8:

  • (8 + 1)(8 - 8) = (9)(0) = 0

Since both substitutions result in 0, we have confirmed that our solutions are correct.