College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 1 - Review Exercises: 42

Answer

$\displaystyle x=\frac{1}{2}\pm\frac{\sqrt{11}}{2}i$

Work Step by Step

We are given: $x^{2}+3=x$ $x^{2}-x+3=0$ We solve using the quadratic formula ($a=1,\ b=-1,\ c=3$): $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ $\displaystyle x=\frac{-(-1)\pm\sqrt{(-1)^{2}-4*1*3}}{2(1)}$ $\displaystyle x=\frac{-(-1)\pm\sqrt{1-12}}{2(1)}$ $\displaystyle x=\frac{+1\pm\sqrt{-11}}{2}$ $\displaystyle x=\frac{1\pm\sqrt{11}i}{2}$ $\displaystyle x=\frac{1}{2}\pm\frac{\sqrt{11}}{2}i$
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