Solve quadratics by inspection, square roots, completing the square, formula, and factoring; express complex solutions.
Reject quadratic solutions that do not make sense in context
Problem
A rectangle has area \(48~\text{square}~\text{units}\), width \(x\), and length \(x+2\). Form and solve the quadratic equation, then use the requirement that a dimension be positive to report the context-valid value of \(x\).
Big Picture
What this problem is really about
The rectangle turns width and length into a quadratic because their product equals the fixed area. We’ll form the area equation, factor it to find both algebraic candidates, then apply the positive-dimension requirement and verify the remaining value in the original geometry.
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