Create and solve one-variable equations and inequalities, including absolute-value, linear, quadratic, simple rational, and exponential cases.
Create and solve a quadratic equation from an area context
Problem
A rectangle has width \(x~\text{units}\), length \(x~+~5~\text{units}\), and area \(84~\text{square}~\text{units}\). Use the displayed dimensions to write and solve the area equation. Report the context-valid root and then the rejected root.
A rectangle has width x, length x + 5, and area 84 square units.Open full size
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What this problem is really about
The rectangle turns the two related dimensions into a quadratic because width times length must equal the given area. We’ll write that area equation, move everything to one side and factor it, then test both algebraic roots against the geometry, where a valid dimension must be positive.
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