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: 18


The trinomial $x^{2}+50x+c$ is a perfect square when $c=625.$ Then $x^{2}+50x+625=(x+25)(x+25)=(x+25)^{2}$

Work Step by Step

$ x^{2}+50x+c\qquad$ ... find half the coefficient of $x$, which is $\displaystyle \frac{50}{2}$. $\qquad$ ...square the result. $(\displaystyle \frac{50}{2})^{2}=\frac{2500}{4}=625\qquad$ ...substitute $c$ with $625$ in the original expression $x^{2}+50x+625=(x+25)^{2}$
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