Math Problem Statement
Solution
The equation shown in the image is:
This is a factored quadratic equation, and to solve it, we can apply the Zero Product Property, which states that if the product of two expressions equals zero, at least one of the expressions must be zero. Thus, we set each factor equal to zero and solve for .
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Set :
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Set :
Therefore, the solutions to the equation are:
Would you like more details or further explanation?
Here are five related questions to explore further:
- How do we expand into standard quadratic form?
- What happens when the quadratic is set to a non-zero value, e.g., ?
- How do you solve quadratics that are not factorable using the quadratic formula?
- What are real-life applications of solving quadratic equations like this one?
- What is the geometric interpretation of the solutions to this quadratic equation?
Tip: When solving quadratic equations, always check if factoring is possible before using more advanced methods like completing the square or the quadratic formula!
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Equations
Factoring
Formulas
Zero Product Property
Quadratic Equation Formula
Theorems
Zero Product Property
Suitable Grade Level
Grades 8-10