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: 54

Answer

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

Work Step by Step

$x^{2}+4x+6=0$ Take the $6$ to the right side of the equation: $x^{2}+4x=-6$ Add $\Big(\dfrac{b}{2}\Big)^{2}$ to both sides of the equation. For this particular case, $b=4$ $x^{2}+4x+\Big(\dfrac{4}{2}\Big)^{2}=-6+\Big(\dfrac{4}{2}\Big)^{2}$ $x^{2}+4x+4=-6+4$ $x^{2}+4x+4=-2$ Factor the left side of the equation, which is a perfect square trinomial: $(x+2)^{2}=-2$ Take the square root of both sides of the equation: $\sqrt{(x+2)^{2}}=\sqrt{-2}$ $x+2=\pm\sqrt{2}i$ Solve for $x$: $x=-2\pm\sqrt{2}i$
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