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
- Read it through. The second number is one more than the first, so one unknown covers both, and their product makes a QUADRATIC.
- Set it up with x for the smaller value: x(x + 1) = 210.
- Look for the whole number that fits — it is 14, because 14 × 15 = 210.
- Answer what was asked — "Find the two numbers.": 14 and 15.
How it works.
- 01
Read it through. The second number is one more than the first, so one unknown covers both, and their product makes a QUADRATIC.
- 02
Set it up with x for the smaller value: x(x + 1) = 210.
- 03
Look for the whole number that fits — it is 14, because 14 × 15 = 210.
- 04
Answer what was asked — "Find the two numbers.": 14 and 15.