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: 59

Answer

$x=-5\pm\sqrt{3}$

Work Step by Step

$x^{2}+10x+28=0$ Take the $28$ to the right side of the equation: $x^{2}+10x=-28$ Add $\Big(\dfrac{b}{2}\Big)^{2}$ to both sides of the equation. In this case, $b=10$ $x^{2}+10x+\Big(\dfrac{10}{2}\Big)^{2}=-28+\Big(\dfrac{10}{2}\Big)^{2}$ $x^{2}+10x+25=-28+25$ $x^{2}+10x+25=-3$ Factor the expression on the left side of the equation, which is a perfect square trinomial: $(x+5)^{2}=-3$ Take the square root of both sides of the equation: $\sqrt{(x+5)^{2}}=\sqrt{-3}$ $x+5=\pm\sqrt{3}i$ Solve for $x$: $x=-5\pm\sqrt{3}$
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