Answer
$x=3$
Work Step by Step
$2x+\sqrt{x+1}=8$
$\sqrt{x+1}=8-2x$
$(\sqrt{x+1})^2=(8-2x)^2$
$x+1=64-32x+4x^2$
$4x^2-32x+64=x+1$
$4x^2-33x+63=0$
$(4x-21)(x-3)=0$
$4x-21=0$
$4x=21$
$4x/4=21/4$
$x=21/4$
$x-3=0$
$x=3$
$2x+\sqrt{x+1}=8$
$2*21/4+\sqrt{21/4+1}=8$
$21/2+\sqrt{25/4}=8$
$10.5+\sqrt{6.25}=8$
$10.5+2.5=8$
$14\ne8$ (false)
$2x+\sqrt{x+1}=8$
$2*3+\sqrt{3+1}=8$
$6+\sqrt 4=8$
$6+2=8$
$8=8$ (true)
