College Algebra (10th Edition)

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

Chapter 1 - Section 1.2 - Quadratic Equations - 1.2 Assess Your Understanding: 82

Answer

The solution set is $\left\{\frac{2}{3}\right\}$.

Work Step by Step

RECALL: A quadratic equation of the form $ax^2+bx+c=0$ can be solved using the quadratic formula $x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$ The given quadratic equation has: $a=9 \\b=-12 \\c=4$ Substitute these values into the quadratic formula to obtain: $x=\dfrac{-(-12) \pm \sqrt{(-12)^2-4(9)(4)}}{2(9)} \\x=\dfrac{12 \pm \sqrt{144-144}}{18} \\x=\dfrac{12\pm \sqrt{0}}{18} \\x =\dfrac{12}{18} \\x=\dfrac{2}{3}$ Therefore, the solution set is $\left\{\frac{2}{3}\right\}$.
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