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(x-8)(x+3)=0

2 min read Jun 17, 2024
(x-8)(x+3)=0

Solving the Equation (x-8)(x+3) = 0

This equation represents a quadratic expression in factored form. To find the solutions for x, 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.

Let's break down the solution:

  1. Identify the factors: The equation is already factored, giving us two factors: (x-8) and (x+3).

  2. Set each factor equal to zero:

    • x - 8 = 0
    • x + 3 = 0

  3. Solve for x in each equation:

    • x = 8
    • x = -3

Therefore, the solutions to the equation (x-8)(x+3) = 0 are x = 8 and x = -3.

Understanding the Solutions:

These solutions represent the points where the graph of the quadratic function intersects the x-axis. In other words, they are the x-intercepts of the parabola.

Visual Representation:

If we were to graph the function represented by the equation, we would see a parabola crossing the x-axis at the points (8, 0) and (-3, 0).

In summary, the solutions to the equation (x-8)(x+3) = 0 are x = 8 and x = -3. These solutions represent the points where the function intersects the x-axis.

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