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: 18


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

Work Step by Step

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