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

2 min read Jun 16, 2024

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

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

The Zero Product Property

The Zero Product 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. In other words:

If a * b = 0, then either a = 0 or b = 0 (or both).

Applying the Property

In our equation, (x+2)(x-7) = 0, we have two factors: (x+2) and (x-7). Applying the Zero Product Property, we set each factor equal to zero and solve for x:

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

Solutions

Therefore, the solutions to the equation (x+2)(x-7) = 0 are x = -2 and x = 7. These are the values of x that make the equation true.

Verification

We can verify our solutions by substituting them back into the original equation:

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

Since both solutions result in 0 when plugged back into the equation, we have confirmed their validity.