Chapter 5 - Section 5.8 - Solving Equations by Factoring and Problem Solving - Exercise Set - Page 323: 52

$x=5$

The factored form of the given expression, $ \dfrac{x^2}{10}+\dfrac{5}{2}=x $, is \begin{array}{l} 10\left( \dfrac{x^2}{10}+\dfrac{5}{2} \right)=(x)10 \\\\ x^2+25=10x \\\\ x^2-10x+25=0 \\\\ (x-5)(x-5)=0 \\\\ (x-5)^2=0 .\end{array} Using the Square Root Property, then \begin{array}{l} x-5=\pm\sqrt{0} \\ x-5=0 \\ x=0+5 \\ x=5 \end{array}