Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter P - Review Exercises - Page 144: 139

Answer

The expression has no real solutions.

Work Step by Step

The expression provided is: $\begin{align} & {{x}^{2}}=2x-19 \\ & {{x}^{2}}-2x+19=0 \end{align}$ Use the following expression, $D={{b}^{2}}-4ac$ Substitute the values in the expression, $\begin{align} & a=1 \\ & b=-2 \\ & c=19 \end{align}$ Now, solve the expression $\begin{align} & D={{b}^{2}}-4ac \\ & ={{\left( -2 \right)}^{2}}-4\left( 1 \right)\left( 19 \right) \\ & =4-76 \\ & =-72 \end{align}$ As, $D<0$ Therefore, the equation has no real solutions.
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