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 - Page 764: 55



Work Step by Step

$2a^{2}+8a=-12$ Take out common factor $2$ from the left side of the equation: $2(a^{2}+4a)=-12$ Take the $2$ to divide the right side of the equation: $a^{2}+4a=\dfrac{-12}{2}$ $a^{2}+4a=-6$ Add $\Big(\dfrac{b}{2}\Big)^{2}$ to both sides of the equation. For this particular case, $b=4$ $a^{2}+4a+\Big(\dfrac{4}{2}\Big)^{2}=-6+\Big(\dfrac{4}{2}\Big)^{2}$ $a^{2}+4a+4=-6+4$ $a^{2}+4a+4=-2$ Factor the left side of the equation, which is a perfect square trinomial: $(a+2)^{2}=-2$ Take the square root of both sides of the equation: $\sqrt{(a+2)^{2}}=\sqrt{-2}$ $a+2=\pm\sqrt{2}i$ Solve for $a$: $a=-2\pm\sqrt{2}i$
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