Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 9 - Quadratic Functions and Equations - 9-5 Completing the Square - Practice and Problem-Solving Exercises - Page 564: 31


$x=13.3$ in

Work Step by Step

Area of a rectangle = Length x Breadth Thus, $(2+x)x=420$ Re-write the equations as: $2x^2+5x=420$ or, $x^2+\frac{5}{2}x=210$ Compare it with the standard form of quadratic equation $ax^2+bx+c$, we have $a=1, b=\frac{5}{2}$ Therefore, $b^2=4ac$ $\implies$ $c=\dfrac{b^2}{4a}$ Thus, $c=\dfrac{b^2}{4a}=\dfrac{(\frac{5}{2})^2}{4}=\dfrac{25}{16}$ To complete the square, add $\dfrac{25}{16}$ on both sides. $x^2+\frac{5}{2}x+\dfrac{25}{16}=210+\dfrac{25}{16}$ $\implies (x+\dfrac{5}{4})^2=\dfrac{3385}{16}$ Neglect negative sigh, we have $\implies (x+\dfrac{5}{4})=14.55$ $x=13.3$ in
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