Rearrange formulas to isolate a chosen quantity, including formulas with quadratic terms.
Rearrange a formula with a squared variable and choose the meaningful square-root branch
Problem
Solve \(A=s^{2}\) for the side length \(s\). Account for the inverse of squaring, then use the geometric meaning of a length to determine the valid branch.
Big Picture
What this problem is really about
Undoing a square algebraically produces both a positive and a negative square-root branch. We’ll write both branches first, then use the fact that s represents a geometric side length to keep only the nonnegative value and verify it by squaring.
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