solve for x

x+√(31-9x)=5

√(31-9x) = 5 - x

square both sides
31 - 9x = 25 - 10x + x^2
x^2 - x - 6 = 0
(x-3)(x+2) = 0
x = 3 or x = -2
BUT, since we squared, we must verify ALL answers

if x = 3
LS = 3 + √4 = 5
RS = 5, YEahh

if x = -2
LS = -2 + √49
= -2 + 7 = 5 = RS, YEAHH

x = -2 or x = 3