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(x+2)(x+1)=0

2 min read Jun 16, 2024
(x+2)(x+1)=0

Solving the Equation (x+2)(x+1) = 0

This equation is a simple quadratic equation in factored form. To find the solutions, we can use the Zero Product Property.

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.

Solving the Equation

In our equation, (x+2)(x+1) = 0, we have two factors: (x+2) and (x+1).

To make the product equal to zero, either one or both of these factors must be zero. So we have two possible cases:

  1. x + 2 = 0 Solving for x, we get x = -2.

  2. x + 1 = 0 Solving for x, we get x = -1.

Solution

Therefore, the solutions to the equation (x+2)(x+1) = 0 are x = -2 and x = -1.

Verification

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

  • For x = -2: (-2 + 2)(-2 + 1) = 0 * 1 = 0
  • For x = -1: (-1 + 2)(-1 + 1) = 1 * 0 = 0

Both solutions satisfy the equation, confirming their validity.

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