(x-2)(x+7)=0

2 min read Jun 17, 2024

Solving the Equation (x-2)(x+7) = 0

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

Understanding the Zero Product Property

The key to solving this equation lies in 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.

In our equation, we have two factors: (x-2) and (x+7). For the product to be zero, either:

(x-2) = 0
(x+7) = 0

Solving for x

Now, we simply solve each of these linear equations:

For (x-2) = 0:
- Add 2 to both sides: x = 2
For (x+7) = 0:
- Subtract 7 from both sides: x = -7

The Solution

Therefore, the solutions to the equation (x-2)(x+7) = 0 are x = 2 and x = -7.

Verification

We can verify our solutions by substituting each value of x back into the original equation:

For x = 2: (2-2)(2+7) = 0 * 9 = 0 (True)
For x = -7: (-7-2)(-7+7) = -9 * 0 = 0 (True)

Both solutions satisfy the equation, confirming our results.