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 - Page 485: 51

Answer

The solutions are $x=-4\pm\sqrt{15}$

Work Step by Step

$x^{2}+8x+1=0$ Take $1$ to the right side: $x^{2}+8x=-1$ Add $\Big(\dfrac{b}{2}\Big)^{2}$ to both sides of the equation. In this particular case, $b=8$: $x^{2}+8x+\Big(\dfrac{8}{2}\Big)^{2}=-1+\Big(\dfrac{8}{2}\Big)^{2}$ $x^{2}+8x+16=-1+16$ $x^{2}+8x+16=15$ Factor the left side of the equation, which is a perfect square trinomial: $(x+4)^{2}=15$ Take the square root of both sides: $\sqrt{(x+4)^{2}}=\pm\sqrt{15}$ $x+4=\pm\sqrt{15}$ Solve for $x$: $x=-4\pm\sqrt{15}$
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