Chapter 11 - Section 11.3 - Solving Equations by Using Quadratic Methods - Exercise Set - Page 788: 39

$x=5$

$x-\sqrt {19-2x}-2=0$ $x-\sqrt {19-2x}-2+\sqrt {19-2x}=0+\sqrt {19-2x}$ $x-2=\sqrt {19-2x}$ $(x-2)^2=(\sqrt {19-2x})^2$ $(x*x+x(-2)+x(-2)+(-2)(-2))=19-2x$ $x^2-4x+4=19-2x$ $x^2-2x-15=0$ $(x-5)(x+3)=0$ $x-5=0$ $x=5$ $x+3=0$ $x=-3$ $x-\sqrt {19-2x}-2=0$ $-3-\sqrt {19-2(-3)}-2=0$ $-3-\sqrt{19+6}-2=0$ $-3-5-2=0$ $-8-2=0$ $-10=0$ (false)