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Solving the Equation (x-3)(x+4) = 0
This equation is a simple quadratic equation in factored form. Let's break down how to solve it and understand the concept behind 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 equation, we have two factors: (x-3) and (x+4). The equation tells us that their product is zero. Therefore, at least one of these factors must be equal to zero.
Solving for x
To find the solutions, we set each factor equal to zero and solve for x:
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(x-3) = 0 Adding 3 to both sides, we get: x = 3
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(x+4) = 0 Subtracting 4 from both sides, we get: x = -4
The Solutions
Therefore, the solutions to the equation (x-3)(x+4) = 0 are x = 3 and x = -4.
Visualizing the Solutions
These solutions represent the x-intercepts of the graph of the quadratic function y = (x-3)(x+4). The graph will cross the x-axis at the points (3,0) and (-4,0).
Summary
Solving the equation (x-3)(x+4) = 0 is a simple application of the Zero Product Property. By setting each factor to zero, we can easily find the solutions which represent the x-intercepts of the corresponding quadratic function.