Algebra: A Combined Approach (4th Edition)

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

Chapter 11 - Section 11.2 - Solving Quadratic Equations by Completing the Square - Exercise Set: 33

Answer

$x=-\dfrac{1}{6}\pm\dfrac{\sqrt{19}}{6}$

Work Step by Step

$x(6x+2)=3$ Evaluate the product on the left side of the equation: $6x^{2}+2x=3$ Take the $3$ to the left side: $6x^{2}+2x-3=0$ Use the quadratic formula to solve this equation. The formula is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Here $a=6$, $b=2$ and $c=-3$. Substitute: $x=\dfrac{-2\pm\sqrt{2^{2}-4(6)(-3)}}{2(6)}=\dfrac{-2\pm\sqrt{4+72}}{12}=...$ $...=\dfrac{-2\pm\sqrt{76}}{12}=\dfrac{-2\pm2\sqrt{19}}{12}=-\dfrac{1}{6}\pm\dfrac{\sqrt{19}}{6}$
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