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 - Guided Practice for Examples 3, 4, and 5 - Page 286: 9


The solutions are $1+2\sqrt{2}$ and $1-2\sqrt{2}$.

Work Step by Step

$ 2n^{2}-4n-14=0\qquad$ ... write left side in the form $x^{2}+bx$ (add $14$ to each side). $ 2n^{2}-4n=14\qquad$ ...divide each term with $2$. $ n^{2}-2n=7\qquad$ ...square half the coefficient of $n$. $(\displaystyle \frac{-2}{2})^{2}=(-1)^{2}=1\qquad$ ...add $1$ to each side of the expression $ n^{2}-2n+1=7+1\qquad$ ...simplify. $ n^{2}-2n+1=8\qquad$ ... write left side as a binomial squared. $(n-1)^{2}=8\qquad$ ...take square roots of each side. $ n-1=\pm\sqrt{8}\qquad$ ...add $1$ to each side $ n-1+1=\pm\sqrt{8}+1\qquad$ ...simplify. $ n=1\pm\sqrt{8}\qquad$ ...rewrite $\sqrt{8}$ as $\sqrt{4\cdot 2.}$ $ n=1\pm\sqrt{4\cdot 2}\qquad$ ...evaluate $\sqrt{4}$. $n=1\pm 2\sqrt{2}$
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