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Solving the Equation (x+5)(x+7) = 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.
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 Zero Product Property
In our equation, (x+5)(x+7) = 0, we have two factors: (x+5) and (x+7).
To make the product equal to zero, at least one of these factors must be zero. Therefore, we can set each factor equal to zero and solve for x:
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x + 5 = 0 Subtracting 5 from both sides gives us: x = -5
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x + 7 = 0 Subtracting 7 from both sides gives us: x = -7
Solutions
Therefore, the solutions to the equation (x+5)(x+7) = 0 are x = -5 and x = -7. These are the values of x that make the equation true.
In conclusion, by applying the Zero Product Property, we have successfully solved the quadratic equation in factored form and found the two solutions for x.