# How do you solve 2x + sqrt(x+1) = 8?

Mar 2, 2016

$x = 3$ or $x = 5.25$
Subtract $2 x$ from bopth sides of the equation, yielding $\sqrt{x + 1} = 8 - 2 x$. Square both sides of the equation, yielding $x + 1 = 64 - 32 x + 4 {x}^{2}$. Subtract x+1 from both sides of the equation, yielding $0 = 63 - 33 x + 4 {x}^{2}$.
 x = (33 (+/-) sqrt(1089 - 4*4*63))/8 = (33 (+/-) sqrt(81))/8 = (33 (+/-) 9)/8.
So, $x = \frac{42}{8}$ or $x = \frac{24}{8}$.