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: 7


The solutions are $-3+\sqrt{5}$ and $-3-\sqrt{5}$

Work Step by Step

$ x^{2}+6x+4=0\qquad$ ... write left side in the form $x^{2}+bx$ (add $-4$ to each side). $ x^{2}+6x+4-4=0-4\qquad$ ...simplify. $ x^{2}+6x=-4\qquad$ ...square half the coefficient of $x$. $(\displaystyle \frac{6}{2})^{2}=3^{2}=9\qquad$ ...add $9$ to each side of the expression $ x^{2}+6x+9=-4+9\qquad$ ... write left side as a binomial squared. $(x+3)^{2}=-4+9\qquad$ ...simplify. $(x+3)^{2}=5\qquad$ ...take square roots of each side. $ x+3=\pm\sqrt{5}\qquad$ ...add $-3$ to each side $ x+3-3=\pm\sqrt{5}-3\qquad$ ...simplify. $x=-3\pm\sqrt{5}$
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