Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 8 - Section 8.1 - Solving Quadratic Equations by Completing the Square - Exercise Set: 35

Answer

The solutions are $x=-5$ and $x=-3$

Work Step by Step

$x^{2}+8x=-15$ Add $\Big(\dfrac{b}{2}\Big)^{2}$ to both sides of the equation. In this particular case, $b=8$: $x^{2}+8x+\Big(\dfrac{8}{2}\Big)^{2}=-15+\Big(\dfrac{8}{2}\Big)^{2}$ $x^{2}+8x+16=-15+16$ $x^{2}+8x+16=1$ Factor the left side of the equation, which is a perfect square trinomial: $(x+4)^{2}=1$ Take the square root of both sides: $\sqrt{(x+4)^{2}}=\pm\sqrt{1}$ $x+4=\pm1$ Solve for $x$: $x=\pm1-4$ $x=-1-4=-5$ $x=1-4=-3$ The solutions are $x=-5$ and $x=-3$
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