Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 11 - Section 11.3 - Integrated Review - Summary on Solving Quadratic Equations: 10

Answer

$x_{1}= -3 + \sqrt{5}$ and $x_{2}= -3 - \sqrt{5}$

Work Step by Step

Given $\dfrac{1}{2}x^2+3x+2=0 \\ $ $a= \dfrac{1}{2}, \ b=3, \ c=2$ Using the quadratic formula: $\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$ we have: $\dfrac{-3 \pm \sqrt{3^2-4 \times \frac{1}{2}\times 2}}{2 \times \frac{1}{2}} = \dfrac{-3 \pm \sqrt{9-4}}{1} = -3 \pm \sqrt{5}$ Therefore, the solutions are $x_{1}= -3 + \sqrt{5}$ and $x_{2}= -3 - \sqrt{5}$
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