Answer
$x=(-3±i\sqrt 7)/8$
Work Step by Step
$(2x+1)^2=x$
$(2x+1)(2x+1)=x$
$2x*2x+2x*1+1*2x+1*1=x$
$4x^2+4x+1=x$
$4x^2+4x+1-x-1=x-x-1$
$4x^2+3x=-1$
$4(x^2+3/4x)=-1$
$4(x^2+3/4x+(3/4*1/2)^2)=-1+4*(3/4*1/2)^2$
$4(x^2+3/4x+9/64)=-1+4*(9/64)$
$4(x+3/8)^2=-1+9/16$
$1/4*4*(x+3/8)^2=-7/16*1/4$
$(x+3/8)^2=-7/64$
$\sqrt {(x+3/8)^2}=\sqrt{-7/64}$
$x+3/8 = ±\sqrt{-7} /\sqrt {64}$
$x+3/8 = ± i\sqrt 7/8$
$x+3/8-3/8 = ± i\sqrt 7/8 – 3/8$
$x=-3±i\sqrt 7 / 8$
