Algebra: A Combined Approach (4th Edition)

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

Chapter 11 - Section 11.1 - Solving Quadratic Equations by Completing the Square - Exercise Set: 56

Answer

$x=-2\pm\sqrt{\dfrac{2}{3}}i$

Work Step by Step

$3x^{2}+12x=-14$ Take out common factor $3$ from the left side of the equation: $3(x^{2}+4x)=-14$ Take the $3$ to divide the left side of the equation: $x^{2}+4x=-\dfrac{14}{3}$ Add $\Big(\dfrac{b}{2}\Big)^{2}$ to both sides of the equation. For this particular case, $b=4$ $x^{2}+4x+\Big(\dfrac{4}{2}\Big)^{2}=-\dfrac{14}{3}+\Big(\dfrac{4}{2}\Big)^{2}$ $x^{2}+4x+4=-\dfrac{14}{3}+4$ $x^{2}+4x+4=-\dfrac{2}{3}$ Factor the left side of the equation, which is a perfect square trinomial: $(x+2)^{2}=-\dfrac{2}{3}$ $\sqrt{(x+2)^{2}}=\sqrt{-\dfrac{2}{3}}$ $x+2=\pm\sqrt{\dfrac{2}{3}}i$ Solve for $x$: $x=-2\pm\sqrt{\dfrac{2}{3}}i$
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