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(x-7)(x+8) 0

2 min read Jun 17, 2024
(x-7)(x+8) 0

Solving the Equation (x-7)(x+8) = 0

This equation is a quadratic equation in factored form. To find the solutions, we can utilize 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.

Here's how we solve the equation:

  1. Set each factor equal to zero:

    • x - 7 = 0
    • x + 8 = 0

  2. Solve for x in each equation:

    • x = 7
    • x = -8

Therefore, the solutions to the equation (x-7)(x+8) = 0 are x = 7 and x = -8.

Understanding the Solutions

These solutions represent the x-intercepts of the parabola that is the graph of the quadratic function y = (x-7)(x+8). This means the graph intersects the x-axis at the points (7, 0) and (-8, 0).

Let's visualize this:

  • Step 1: Expand the equation:

    • (x-7)(x+8) = x² + x - 56

  • Step 2: Graph the function y = x² + x - 56. You'll find that the parabola intersects the x-axis at x = 7 and x = -8.

In summary, solving the equation (x-7)(x+8) = 0 involves finding the values of x that make the expression equal to zero. This is done by applying the Zero Product Property and solving for x in each factor.

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