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Solving the Equation: (x+3)(x-8) = 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.
The Zero Product Property
This 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) and (x-8) are the two factors. Therefore, we have two possibilities:
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x + 3 = 0
Solving for x, we get: x = -3 -
x - 8 = 0 Solving for x, we get: x = 8
Solutions
Therefore, the solutions to the equation (x+3)(x-8) = 0 are x = -3 and x = 8.
Verification
We can verify these solutions by plugging them back into the original equation:
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For x = -3: (-3 + 3)(-3 - 8) = (0)(-11) = 0
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For x = 8: (8 + 3)(8 - 8) = (11)(0) = 0
Both solutions satisfy the equation, confirming our results.
Conclusion
By applying the Zero Product Property, we successfully solved the equation (x+3)(x-8) = 0, finding the two solutions: x = -3 and x = 8. This demonstrates the effectiveness of factoring in solving quadratic equations.