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

Jasonbradley

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Jun 16, 2024

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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 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 case, we have two factors: (x+5) and (x+2). Therefore, for the entire equation to equal zero, at least one of these factors must be zero.

Finding the Solutions

1. Set each factor equal to zero:

   • x + 5 = 0
   • x + 2 = 0

2. Solve for x in each equation:

   • x = -5
   • x = -2

The Solutions

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

Verification

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

• For x = -5: (-5 + 5)(-5 + 2) = (0)(-3) = 0
• For x = -2: (-2 + 5)(-2 + 2) = (3)(0) = 0

Since both substitutions result in zero, we have confirmed that our solutions are correct.