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

2 min read Jun 17, 2024

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

This equation is a simple example of a quadratic equation in factored form. To solve for the values of x that satisfy the equation, we can use the Zero Product Property.

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-2) and (x+5) are the two factors. Therefore, for the product to be zero, either:

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

Solving for x

Let's solve each equation individually:

(x-2) = 0
- Add 2 to both sides: x = 2
(x+5) = 0
- Subtract 5 from both sides: x = -5

The Solutions

Therefore, the solutions to the equation (x-2)(x+5) = 0 are x = 2 and x = -5. These values make the equation true when substituted back into the original equation.

Visualizing the Solutions

We can visualize these solutions graphically. The equation (x-2)(x+5) = 0 represents a parabola that intersects the x-axis at x = 2 and x = -5. These points of intersection are the roots or solutions of the equation.