9.1.1 Equations with Quadratic Expressions on Both Sides of the Equal Sign

Algebra 19.1.1 Equations with Quadratic Expressions on Both Sides of the Equal Sign

Search for key terms or text.

9.1.1 • Equations with Quadratic Expressions on Both Sides of the Equal Sign

Warm Up

In each equation, what expression could be substituted for $a$ so the equation is true for all values of $x$ ?

$x^{2} = a^{2}$

Compare your answer:

$a = x$ .

$(3 x)^{2} = a^{2}$

Compare your answer:

$a = 3 x$ .

$a^{2} = 7 x \cdot 7 x$

Compare your answer:

$a = 7 x$ .

$25 x^{2} = a^{2}$

Compare your answer:

$a = 5 x$ .

$a^{2} = \frac{1}{4} x^{2}$

Compare your answer:

$a = \frac{1}{2} x$ .

$a^{2} = (x + 1)^{2}$

Compare your answer:

$a = x + 1$ .

$(2 x - 9) (2 x - 9) = a^{2}$

Compare your answer:

$a = 2 x - 9$ .

Previous Next

Order a print copy

Citation/Attribution

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution-NonCommercial-ShareAlike License and you must attribute OpenStax.

Attribution information

If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:
Access for free at https://openstax.org/books/algebra-1/pages/about-this-course
If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:
Access for free at https://openstax.org/books/algebra-1/pages/about-this-course

Citation information

Use the information below to generate a citation. We recommend using a citation tool such as this one.
- Authors: Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis, Jay Abramson, Sharon North, Amy Baldwin, Alyssa Howell
- Publisher/website: OpenStax
- Book title: Algebra 1
- Publication date: Jun 4, 2025
- Location: Houston, Texas
- Book URL: https://openstax.org/books/algebra-1/pages/about-this-course
- Section URL: https://openstax.org/books/algebra-1/pages/9-1-1-equations-with-quadratic-expressions-on-both-sides-of-the-equal-sign

© Aug 26, 2025 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.