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: 34

Answer

$x=-\dfrac{1}{14}\pm\dfrac{\sqrt{57}}{14}$

Work Step by Step

$x(7x+1)=2$ Evaluate the product on the left side of the equation: $7x^{2}+x=2$ Take the $2$ to the left side of the equation: $7x^{2}+x-2=0$ Use the quadratic formula to solve this equation. The formula is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Here, $a=7$, $b=1$ and $c=-2$. Substitute: $x=\dfrac{-1\pm\sqrt{1^{2}-4(7)(-2)}}{2(7)}=\dfrac{-1\pm\sqrt{1+56}}{14}=...$ $...=\dfrac{-1\pm\sqrt{57}}{14}=-\dfrac{1}{14}\pm\dfrac{\sqrt{57}}{14}$
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