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 289: 53


The solutions are $-\displaystyle \frac{3}{2}+i\frac{\sqrt{47}}{2}$ and $-\displaystyle \frac{3}{2}-i\frac{\sqrt{47}}{2}$.

Work Step by Step

$ x^{2}+3x+14=0\qquad$ ...Write left side in the form $x^{2}+bx.$(add $-14$ to each side) $ x^{2}+3x=-14\qquad$ ...square half the coefficient of $x$. $(\displaystyle \frac{3}{2})^{2}=\frac{9}{4}\qquad$ ...complete the square by adding$ \displaystyle \frac{9}{4}$ to each side of the expression $ x^{2}+3x+\displaystyle \frac{9}{4}=-14+\frac{9}{4}\qquad$ ...Write left side as a binomial squared. $(x+\displaystyle \frac{3}{2})^{2}=\frac{-47}{4}\qquad$ ...take square roots of each side. $ x+\displaystyle \frac{3}{2}=\pm i\sqrt{\frac{47}{4}}\qquad$ ...simplify $i\displaystyle \sqrt{\frac{47}{4}}=i\frac{\sqrt{47}}{\sqrt{4}}=i\frac{\sqrt{47}}{2}$ $ x+\displaystyle \frac{3}{2}=\pm i\frac{\sqrt{47}}{2}\qquad$ ...add $-\displaystyle \frac{3}{2}$ to each side. $x=-\displaystyle \frac{3}{2}\pm i\frac{\sqrt{47}}{2}$
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