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Solving the Equation (x + 7)(x + 3) = 0
This equation represents a quadratic equation in factored form. To find the solutions for x, we can use 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.
Applying the Zero Product Property
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Set each factor equal to zero:
- x + 7 = 0
- x + 3 = 0
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Solve each equation for x:
- x = -7
- x = -3
Solutions
Therefore, the solutions to the equation (x + 7)(x + 3) = 0 are x = -7 and x = -3.
Interpretation
These solutions represent the x-intercepts of the parabola represented by the quadratic equation. In other words, the graph of the equation will cross the x-axis at the points (-7, 0) and (-3, 0).
Expanding the Equation
If we expand the equation (x + 7)(x + 3) = 0, we get the standard quadratic form:
x² + 10x + 21 = 0
This equation represents the same parabola as the factored form, but it's expressed differently. We can solve this equation using the quadratic formula or factoring techniques as well.