Math Problem Statement
Solve the equation: 2x^2-4x-7=0 . Fully simplify all answers, including non-real solutions.
Solution
To solve the quadratic equation , we will use the quadratic formula:
Step 1: Identify coefficients
From the equation :
Step 2: Plug into the quadratic formula
Simplify each term:
Step 3: Simplify the square root
Thus:
Step 4: Split into two terms
Final Answer:
These are the two simplified solutions. If non-real solutions existed, they would have appeared during the square root calculation. In this case, the solutions are real.
Would you like me to graph the equation or explain the solution in more detail? 😊
5 Related Questions:
- How do you derive the quadratic formula from a general quadratic equation?
- What is the geometric interpretation of the solutions to ?
- Can quadratic equations have only one solution? If so, under what conditions?
- What happens when the discriminant () is negative?
- How can the quadratic formula be used in real-world problems?
Tip:
Always simplify the square root in a quadratic solution as much as possible to ensure your answer is in its most concise form!
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Equations
Simplifying Square Roots
Formulas
Quadratic formula: x = (-b ± √(b² - 4ac)) / 2a
Theorems
Properties of square roots
Discriminant analysis in quadratic equations
Suitable Grade Level
Grades 9-10
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