Algebra: A Combined Approach (4th Edition)

Published by Pearson

Chapter 11 - Section 11.1 - Solving Quadratic Equations by Completing the Square - Practice - Page 759: 7

Answer

$x = (-4-\sqrt 17, -4+\sqrt 17)$

Work Step by Step

Step -1 : Add the square of half of the co-efficient of x to both sides. Co-efficient of x = 8 Half of 8 = $\frac{1}{2}\times8 = 4$ Square of 4 is $4 \times4 = 16$ The equation becomes $x^2+8x+16=1 +16$ Step-2 Factor the trinomial and simplify the right hand side. $(x+4)^2= 17$ Step-3 Use the square root property and solve for $x$ $x+4=±\sqrt 17$ Step-4 Subtract 4 on both the sides $x=-4±\sqrt 17$ Therefore the solution set is $(-4-\sqrt 17, -4+\sqrt 17)$

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