College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 1, Equations and Graphs - Section 1.9 - Solving Equations and Inequalities Graphically - 1.9 Exercises - Page 158: 20

Answer

The solutions are $x=\left\{-1, -0.25, 0.25\right\}$.

Work Step by Step

To solve the given equation graphically, perform the following steps: (1) Graph the functions $y=16x^3+16x^2$ (red graph) and $y=x+1$ (blue graph) using a graphing utility. Refer to the image below for the graph. (2) Identify the point/s where the graphs intersect each other. These are the points where the value of $16x^3+16x^2$ is equal tot he value of $y=x+1$ are equal.. The x-coordinates of these points are the solutions to the given equation. Notice that the graphs intersect at the points $(-1, 0)$, $(-0.25, 0.75)$, and $(0.25, 1.25)$. This means that the solutions to the given equation are $-1, -0.25, $ and $0.25$. Thus, the solutions are $x=\left\{-1, -0.25, 0.25\right\}$.
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