AlgebraStructure & Method · Book 1All Chapters

Using Quadratic Equations

12-6Solving Problems Involving Quadratic Equations

Overview

Set up a quadratic from a problem, solve it, and discard unreasonable solutions.

Key ideas

  • Define the variable carefully.
  • Translate to a quadratic.
  • Check that solutions fit the context (positive lengths, etc.).

Worked examples

Example 1

Problem. A rectangle’s length is 4 more than its width; its area is 60. Find dimensions.

Solution. w(w + 4) = 60 → w² + 4w − 60 = 0 → (w + 10)(w − 6) = 0 → w = 6, length = 10.

Practice

Try each one. Click Show answer when ready.

  1. 1.

    n(n + 5) = 84. Find n.

  2. 2.

    Square’s area is 81. Side?

  3. 3.

    Rectangle: width = x, length = x + 3, area = 28. Find x.

Challenge problems

A little tougher — great for test prep. Click Show answer when ready.

  1. 1.

    The product of two consecutive positive even integers is 168. Find the integers.

  2. 2.

    A rectangle's length is 5 more than its width. The area is 84. Find the dimensions.