Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 4 Quadratic Functions and Factoring - 4.7 Complete the Square - 4.7 Exercises - Skill Practice - Page 288: 21


The trinomial $x^{2}-x+c$ is a perfect square when $c=\displaystyle \frac{1}{4}.$ Then $ x^{2}-x+\displaystyle \frac{1}{4}=(x-\frac{1}{2})(x-\frac{1}{2})=(x-\frac{1}{2})^{2}$.

Work Step by Step

$ x^{2}-x+c\qquad$ ... find half the coefficient of $x$, which is $\displaystyle \frac{-1}{2}$. $\qquad$ ...square the result. $(\displaystyle \frac{-1}{2})^{2}=\frac{1}{4}\qquad$ ...substitute $c$ with $\displaystyle \frac{1}{4}$ in the original expression $x^{2}-x+\displaystyle \frac{1}{4}=(x-\frac{1}{2})^{2}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.