Quadratic equation word problems, step by step

A quadratic turns up the moment a problem multiplies an unknown by itself.

The question

Find the two numbers.

Two consecutive counting numbers have a product of 210.
x(x + 1) = 210
14 × 15 = 210
asked:Find the two numbers.
14 and 15
  1. Read it through. The second number is one more than the first, so one unknown covers both, and their product makes a QUADRATIC.
  2. Set it up with x for the smaller value: x(x + 1) = 210.
  3. Look for the whole number that fits — it is 14, because 14 × 15 = 210.
  4. Answer what was asked — "Find the two numbers.": 14 and 15.

How it works.

  1. 01

    Read it through. The second number is one more than the first, so one unknown covers both, and their product makes a QUADRATIC.

  2. 02

    Set it up with x for the smaller value: x(x + 1) = 210.

  3. 03

    Look for the whole number that fits — it is 14, because 14 × 15 = 210.

  4. 04

    Answer what was asked — "Find the two numbers.": 14 and 15.