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

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

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

This equation is a simple quadratic equation that can be solved using the Zero Product Property. This property states that if the product of two or more factors is equal to zero, then at least one of the factors must be equal to zero.

Let's break down the steps:

  1. Identify the factors: The equation is already factored, giving us two factors: (x-2) and (x+8).

  2. Set each factor equal to zero:

    • x - 2 = 0
    • x + 8 = 0

  3. Solve for x:

    • x = 2
    • x = -8

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

Understanding the Zero Product Property

The Zero Product Property is a fundamental concept in algebra. It allows us to solve equations by breaking them down into simpler factors. This property is crucial for solving various equations, including quadratic equations, polynomial equations, and even equations involving trigonometric functions.

Applications of Solving Quadratic Equations

Solving quadratic equations like this one has numerous applications in various fields, including:

  • Physics: Calculating the trajectory of projectiles, determining the position of objects in motion, and analyzing the behavior of springs and pendulums.
  • Engineering: Designing structures, bridges, and other engineering projects that require understanding the behavior of forces and stresses.
  • Finance: Modeling financial growth, calculating interest rates, and analyzing investment strategies.
  • Computer science: Developing algorithms and optimizing computer programs.

By understanding how to solve quadratic equations, we can unlock a wide range of mathematical and scientific concepts.

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