(x%2B7)%3D0.jpeg "(x-3)(x+7)=0")
Solving the Equation (x-3)(x+7) = 0
This equation represents a quadratic expression in factored form. To solve for the values of x that satisfy the equation, 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 equal to zero, then at least one of the factors must be equal to zero.
Applying the Property
In our equation, (x-3)(x+7) = 0, we have two factors: (x-3) and (x+7). According to the Zero Product Property, for the product to be zero, at least one of these factors must equal zero.
Therefore, we have two possible cases:
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Case 1: (x-3) = 0 Solving for x, we get x = 3.
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Case 2: (x+7) = 0 Solving for x, we get x = -7.
Solutions
Thus, the solutions to the equation (x-3)(x+7) = 0 are x = 3 and x = -7.
These solutions represent the x-intercepts of the parabola represented by the quadratic equation. In other words, the graph of the equation intersects the x-axis at the points (3, 0) and (-7, 0).