(x+10)(x-2)=0

Jasonbradley

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Jun 16, 2024

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Solving the Equation: (x + 10)(x - 2) = 0

This equation represents a quadratic equation in factored form. To solve for the values of x that satisfy the equation, we can utilize 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.

Let's apply this to our equation:

(x + 10)(x - 2) = 0

This means either:

• (x + 10) = 0
  Solving for x, we get x = -10

• (x - 2) = 0 Solving for x, we get x = 2

Therefore, the solutions to the equation (x + 10)(x - 2) = 0 are x = -10 and x = 2.

Understanding the Concept

The factored form of the equation reveals the x-intercepts of the corresponding quadratic function. The x-intercepts are the points where the graph of the function crosses the x-axis. In this case, the graph will cross the x-axis at x = -10 and x = 2.

In summary:

• The Zero Product Property is a powerful tool for solving quadratic equations in factored form.
• By setting each factor equal to zero and solving for x, we find the solutions to the equation.
• The solutions represent the x-intercepts of the corresponding quadratic function.