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Quadratic equation word problems worksheets

A quadratic turns up the moment a problem multiplies an unknown by itself — an area, or a product of two numbers a step apart. These free printable worksheets give those situations and ask a child to set up the equation and find the value.

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Quadratic equation word problems
Quadratic equation word problems worksheet — Rectangle area, consecutive product, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

Two shapes, both landing on whole answers. A rectangle is a few meters longer than it is wide with a given area, which is x times (x + k) equals the area; two consecutive numbers have a given product, which is x times (x + 1). Each is the everyday place a quadratic actually comes from, rather than an abstract square handed over with no reason to exist.

Why this sheet works

Every constant is built from a whole solution, so the equation always factors over the integers and the answer is a length a child can check — never 4.7 meters. Both shapes ask for both values by name, the width and the length or the two numbers, so a student sets up the equation, solves for one, and reads off the other.

How this one works

One question from a sheet like this one, worked a step at a time — with a sentence saying what just happened and why.

Quadratic equation word problems, step by step

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