Solve by Extraneous : sqrt x+7-x=1

√ (x+7) - x=1

√ (x+7) = x+1

[√ (x+7) ]² = (x+1) ²

x+7=x²+2x+1

x²+x-6=0

x=[-1⁺₋√ (1+24) ]/2 = (-1⁺₋5) / 2

We have two possible solutions:

x₁ = (-1-5) / 2=-6/2=-3

x₂ = (-1+5) / 2=4/2=2

We must check the answer:

if x₁=-3 ⇒√ (x+7) - x=√4 + 3=2+3=5≠1; then x₁=-3 is not a solution for this equation.

if x₂=2; ⇒√ (x+7) - x=√9-2=3-2=1; then x₂=2 is a solution for this equation.

answer: the only one solution is x=2;