Questions and Answers
What is the solution to the equation that results in x = 32?
What are the possible solutions to the equation resulting in x = ±125?
What is the solution for x if x = 20 (x ≠ 5)?
What is the solution if x = 5 (x ≠ -2)?
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What is the solution for x when x = 67?
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What are the solutions if x = 1 or x = 3?
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What is the solution for x if x = 3 (x ≠ -2)?
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What is the solution to the equation when x = 4?
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What is the solution for x if x = 44?
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What is the solution when x = 8?
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What is the solution when x = 3?
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What is the solution when x = -1?
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What is the solution to the radical equation √x = 7?
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What is the solution for the equation 4 = √-2y?
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What is the solution to the equation √(2x - 5) = 7?
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What is the solution for the equation √(x - 7) = 3?
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What is the solution to the equation -10 + √x = 5?
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What is the solution to the equation 4√(2x - 1) = 12?
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What is the solution for √(12x - 3) = √(4x + 93)?
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What is the solution for √(x - 1) = √(3x - 5)?
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What is the solution for the equation 5 = √(x + 1)?
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What is the solution when 2 = √(-2x)?
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What is the solution to the equation √(4x - 8) = 6?
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What is the solution to 4 + √(x + 10) = 12?
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What is the solution to √(4x - 8) = √(x + 3)?
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What is the solution to ∛(2x + 14) = 4?
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What are the solutions to the equation √(8x - 15) = x?
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What is the solution to the equation √(2x + 24) = x?
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What is the solution for the equation √(3x + 28) - x = 0?
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What is the solution for -4 ³√(x + 10) + 3 = 15?
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What is the solution for (c + 2)¾ - 1 = 7?
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What is the solution when √(7x + 15) = x + 1?
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Study Notes
Solving Radical Equations
- Solutions to radical equations must be verified for extraneous roots which can appear during the solving process.
- Various forms of solutions include single values, positives and negatives, or multiple disallowed values.
Specific Solutions
- x = 32: A straightforward radical equation with no extraneous solutions.
- x = ±125: Indicates two possible solutions; check for extraneous values.
- x = 20 (x ≠ 5) and x = 5 (x ≠ -2): Requires verification to exclude invalid results.
- x = 67, x = 44, x = 1 or 3, x = 4, x = 8, x = 3 (x ≠ -2), x = 12: All solutions require extraneous checks.
- x = -1, x = 49, x = -8: Solutions obtained from solving simple radical equations, some needing verification for extraneous results.
- x = 27: Result from the equation √(2x - 5) = 7.
- x = 16: Obtained from solving √(x - 7) = 3.
- x = 225: Derived from -10 + √x = 5.
- x = 5: Found through the equation 4√(2x - 1) = 12.
- x = 2: Result from √(x - 1) = √(3x - 5).
- x = 24: Solution to 5 = √(x + 1).
- x = -2: From the equation 2 = √(-2x).
- x = 11, x = 54, x = 11/3, x = 25: Each of these results comes from different radical equations requiring careful investigation of all potential solutions.
Critical Concepts
- Solutions may appear valid but must be tested against the criteria of the original equation.
- Disallowed values (e.g., x ≠ -2) indicate restrictions based on radical equations, preventing certain solutions from being legitimate.
- Certain problems involve cube roots (e.g., x = 25 from ∛(2x + 14) = 4) which expands the type of radical equations encountered.
General Strategy
- Isolate the radical expression before squaring both sides to eliminate the root.
- Retain attention on the potential for extraneous solutions that could arise from the squaring process.
- Always simplify and communicate solutions clearly, addressing any restrictions explicitly.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge of solving radical equations with these flashcards designed for Algebra 2 students. Each card presents a unique equation to solve while reminding you to check for extraneous solutions. This quiz will reinforce your understanding of key concepts in radical equations.
