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(x-5)(x+2)=0

2 min read Jun 17, 2024
(x-5)(x+2)=0

Solving the Equation (x-5)(x+2) = 0

This equation represents a quadratic equation in factored form. Let's break down how to solve it:

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-5) and (x+2) are the factors. Therefore, for the product to be zero, at least one of these factors must be equal to zero.

Solving for x

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

  • x - 5 = 0

    • Adding 5 to both sides, we get: x = 5

  • x + 2 = 0

    • Subtracting 2 from both sides, we get: x = -2

Solutions

Therefore, the solutions to the equation (x-5)(x+2) = 0 are:

  • x = 5
  • x = -2

These solutions represent the x-intercepts of the parabola that the quadratic equation represents.

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