Chapter 11 - Section 11.3 - Solving Equations by Using Quadratic Methods - Exercise Set - Page 788: 36

$x=-3/8, 1/2$

$4x=\sqrt {2x+3}$ $(4x)^2=(\sqrt {2x+3})^2$ $16x^2=2x+3$ $16x^2-2x-3=0$ $x=(-b±\sqrt{b^2-4ac})/2a$ $x=(-(-2)±\sqrt{(-2)^2-4*16*(-3)})/2*16$ $x=(2±\sqrt{4+4*16*3})/32$ $x=(2±\sqrt{4+192})/32$ $x=(2±\sqrt{196})/32$ $x=(2±14)/32$ $x=(2±14)/32$ $x=(2+14)/32$ $x=16/32$ $x=1/2$ $x=(2±14)/32$ $x=(2-14)/32$ $x=-12/32$ $x=-6/16$ $x=-3/8$