Math Problem Statement
Solution
To solve the quadratic equation using the quadratic formula, we start with the standard form of the quadratic equation:
Here, , , and .
The quadratic formula is:
Substitute the values of , , and :
Simplify this step by step:
- Calculate the discriminant:
- Plug the discriminant back into the quadratic formula:
- Simplify further:
- Calculate the approximate decimal values (rounded to two decimal places):
Thus, the solution set is:
Would you like more details on any of these steps, or do you have any questions?
Here are 5 relative questions:
- What is the discriminant and how does it affect the number of real solutions?
- How does the quadratic formula apply to equations where the coefficient is not 1?
- Can the quadratic formula be used for complex solutions? If so, how?
- What are some alternative methods to solve quadratic equations besides the quadratic formula?
- How would the solution set change if were positive instead of negative?
Tip: Always check the discriminant first before proceeding with the quadratic formula, as it will tell you whether real solutions exist.
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Math Problem Analysis
Mathematical Concepts
Quadratic Equations
Quadratic Formula
Discriminant
Formulas
Quadratic formula
Theorems
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Suitable Grade Level
Grades 10-12