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(x-8)(x+2)=0

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

Solving the Equation: (x-8)(x+2) = 0

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

Understanding the 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.

In our equation, (x-8) and (x+2) are the factors. Therefore, for the entire product to equal zero, at least one of these factors must be zero.

Solving for x

We can set each factor equal to zero and solve for x:

  • Factor 1: (x - 8) = 0

    • Add 8 to both sides: x = 8

  • Factor 2: (x + 2) = 0

    • Subtract 2 from both sides: x = -2

The Solution

Therefore, the solutions to the equation (x-8)(x+2) = 0 are x = 8 and x = -2.

These values represent the points where the graph of the quadratic function represented by the equation would intersect the x-axis (also known as the roots or zeroes of the function).

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