Solve the quadratic equation (5x - 25)(x + 6) = 0 using the Zero Product Property. The solutions for x are __________.
Answer & Analysis
Analysis
Question Analysis
This question assesses the student's ability to apply the Zero Product Property to solve a quadratic equation. The given equation is already factored, and the student needs to set each factor equal to zero and solve for .
Key Concept Explanation
The Zero Product Property is a crucial tool in solving quadratic equations. It states that if the product of two or more factors is zero, then at least one of the factors must be zero. This property allows us to convert a quadratic equation into linear equations, which are easier to solve.
Step-by-step Solution
1. Given the equation:
2. Apply the Zero Product Property: Set each factor equal to zero.
or
3. Solve each linear equation separately:
For
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