Math Problem Statement
Solution
The image you've uploaded contains a mathematical problem that asks to find the value of when the given expression is simplified. The expression provided is:
Let's solve this step by step.
Step 1: Simplify the equation
First, subtract from both sides to move all the terms to one side:
This simplifies to:
Step 2: Factor the equation
The equation can be further simplified by factoring out the common term:
This can be factored further:
Step 3: Solve for
Now, set each factor equal to zero:
So, the solutions are:
Final Answer
The value of can be either or .
Would you like more details on the steps, or do you have any questions?
Further Exploration:
- How would you verify the solutions by substituting back into the original equation?
- Can you solve a similar equation where the quadratic term has a different coefficient?
- What happens if the constant term was different? How would that affect the solution?
- What if the equation was not factorable by simple methods? What technique would you use?
- Can you explain how the discriminant of a quadratic equation determines the number of solutions?
Tip:
When factoring quadratic equations, always check if the quadratic can be simplified first, as it can save you from unnecessary complexity.
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Equations
Factoring
Formulas
Quadratic equation: ax^2 + bx + c = 0
Theorems
Zero Product Property
Suitable Grade Level
Grades 9-10