Question #6451228Fill in the Blank
Algebra-2
Question
Solve the equation and find the value of x.
Answer & Analysis
Analysis
Question Analysis
This question involves a square root radical equation where the radical and linear term are set equal (after rearranging). The main focus is on isolating the radical, squaring to eliminate it, solving the quadratic equation, and verifying solutions to reject extraneous roots.
This question involves a square root radical equation where the radical and linear term are set equal (after rearranging). The main focus is on isolating the radical, squaring to eliminate it, solving the quadratic equation, and verifying solutions to reject extraneous roots.
Key Concept Explanation
Isolation First: Rearrange to —the RHS (x) must be non-negative ( ) because square roots are non-negative.
Quadratic Result: Squaring both sides produces a quadratic equation, and only solutions that satisfy and the original equation are valid.
Isolation First: Rearrange to —the RHS (x) must be non-negative ( ) because square roots are non-negative.
Quadratic Result: Squaring both sides produces a quadratic equation, and only solutions that satisfy and the original equation are valid.
Step-by-step Solution
1. Isolate the radical: (since for validity).
2. Square both sides: .
3. Rearrange to standard quadratic form:
1. Isolate the radical: (since for validity).
2. Square both sides: .
3. Rearrange to standard quadratic form:
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