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

Jasonbradley

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Jun 17, 2024

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

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

Understanding 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. This is the key to solving our equation.

Applying the Zero Product Property

1. Identify the factors: In our equation, (x+7) and (x-2) are the factors.
2. Set each factor equal to zero:
   • x + 7 = 0
   • x - 2 = 0
3. Solve for x in each equation:
   • x = -7
   • x = 2

Solutions

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

Checking Our Solutions

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

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

Since both solutions result in 0, we have verified that they are correct.