x - sqrt(x+5) = 7...........rearrange the equation

x - 7 = sqrt(x+5)...........square the equation

x^2 - 14x + 49 = x + 5...simplify the equation

x^2 - 15x + 44 = 0.........factor the equation as a quadratic trinomial

(x - 11) * (x - 4) = 0.......test solutions to quadratic

11 - sqrt(11+5) = 7 (correct)

and

4 - sqrt(4+5) =/= 7 (incorrect)

11 is the answer.

√ (x+5) = x - 7

squaring both side

x +5 = x^2 -14x +49

x^2 -15 x +44 = 0

x^2 -11x -4 x + 44 =0

x(x-11) - 4(x - 11) =0

(x-11) (x-4) =0

x = 4 and x = 11

but x = 4 does not satisfy, therefore x = 11..................................Ans