Question #6451234Fill in the Blank
Algebra-2
Question
Solve the equation and find the value of x.
Answer & Analysis
Analysis
Question Analysis
This problem involves a square root radical equation with a linear term on both sides. The main focus is on squaring to eliminate the radical, solving the resulting quadratic, and verifying solutions to reject extraneous roots (critical for square roots).
This problem involves a square root radical equation with a linear term on both sides. The main focus is on squaring to eliminate the radical, solving the resulting quadratic, and verifying solutions to reject extraneous roots (critical for square roots).
Key Concept Explanation
Radical + Quadratic Link: Squaring (where ) gives a quadratic equation. For , the RHS ( ) must be non-negative ( ) to avoid undefined square roots.
Extraneous Roots: Quadratic solutions may not satisfy the original equation, so verification is mandatory.
Radical + Quadratic Link: Squaring (where ) gives a quadratic equation. For , the RHS ( ) must be non-negative ( ) to avoid undefined square roots.
Extraneous Roots: Quadratic solutions may not satisfy the original equation, so verification is mandatory.
Step-by-step Solution
1. Confirm RHS non-negativity: .
2. Square both sides: .
3. Rearrange to quadratic form: .
4. Solve for x: or
1. Confirm RHS non-negativity: .
2. Square both sides: .
3. Rearrange to quadratic form: .
4. Solve for x: or
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