Question

(square root x+7)-x=1

Answer 1

\[\sqrt{x+7}-x=1\]
add x to both sides
\[\sqrt{x-7}=x+1\]
sqare both sides
\[x-7=(x+1)^2=x^2+2x+1\]
set 0= 0
\[x^2+x-6=0\]
factor
\[(x+3)(x-2)=0\]
solve
\[x+3=0\]
\[x=-3\]
or \[x-2=0\]
\[x=2\]
now check

Answer 2

2 works because
\[\sqrt{2+7}-2=\sqrt{9}-2=3-2=1\]

Answer 3

-3 does not work because
\[\sqrt{-3+7}-(-3)=\sqrt{4}+3=2+3=5\]

Answer 4

Thank you

Answer 5

welcome