Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 9 - Quadratic Functions and Equations - 9-5 Completing the Square - Practice and Problem-Solving Exercises - Page 580: 32


Width of walkway,$x=3.1$ ft

Work Step by Step

Area of the walkway=$(2x+42)(2x+26)-26 \times 42$ Thus, $4x^2+136x=460$ Re-write the equations as: $x^2+34x=115$ Compare it with the standard form of quadratic equation $ax^2+bx+c$, we have $a=1, b=34$ To complete the square, add $\dfrac{(34)^2}{4}=289$ on both sides. $x^2+34x+289=115+289$ $\implies (x+17)^2=404$ Neglecting the negative sign, we have $\implies (x+17)=20.1$ $x=3.1$ ft Width of walkway,$x=3.1$ ft
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