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: 10


The solutions are $u=\displaystyle \frac{-1+5\sqrt{3}}{2}$ or $u=\displaystyle \frac{-1-5\sqrt{3}}{2}$.

Work Step by Step

$ 4u^{2}+4u+1=75\qquad$ ...write left side as a binomial squared.($(a+b)^{2}=a^{2}+2ab+b^{2}$) $a=2u,b=1$ $(2u+1)^{2}=75\qquad$ ...take square roots of each side. $ 2u+1=\pm\sqrt{75}\qquad$ ...add $-1$ to each side. $ 2u+1-1=\pm\sqrt{75}-1\qquad$ ...simplify. $ 2u=-1\pm\sqrt{75}\qquad$ ...rewrite $\sqrt{75}$ as$ \sqrt{25}\cdot\sqrt{3}2$ $ 2u=-1\pm\sqrt{25}\cdot\sqrt{3}\qquad$ ...evaluate $\sqrt{25}$. $ 2u=-1\pm 5\sqrt{3}\qquad$ ...divide both sides with $2$. $ u=\displaystyle \frac{-1\pm 5\sqrt{3}}{2}\qquad$ ...write as separate equations. $u=\displaystyle \frac{-1+5\sqrt{3}}{2}$ or $u=\displaystyle \frac{-1-5\sqrt{3}}{2}$
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