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

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.

the only one solution is x=2;

11 mintues is the naswer