√110 -n=n. Please solve this question with its steps. Thanks.?

I assume the left side is all under the square root. You should use parentheses to clarify this:
√(110 - n) = n

Square both sides:
110 - n = n²

Get everything on one side:
n² + n - 110 = 0

Factor:
(n + 11)(n - 10) = 0

Possible solutions:
n = -11
n = 10

But we need to check for extraneous solutions and eliminate them. Since the √ symbol asks for the *principal* (non-negative) square root, we need n to be positive. That would eliminate -11 as an answer.

Double-check:
√(110 - (-11)) =? -11
√121 =? -11
11 = -11 (extraneous solution, eliminate -11)

√(110 - 10) =? 10
√100 =? 10
10 = 10 (correct)

Answer:
n = 10

√110 -n = n ... is the entire left side under the radical???
√(110 -n) = n ... square both sides
110 - n = n^2
n^2 + n - 110 = 0
(n + 11)(n - 10) = 0
n = -11 or n = 10
check for extraneous solutions ... not true ... extraneous n = -11
n = 10 <<< only solution

The way that you typed it....

√110=2n

110=4n^2

n^2=27.5

n~±5.244 depending on whether √110 is positive or negative...

If -√110 then n=-5.244 and if √110 then n=5.244

sqrt(110) - n = n
n + n = sqrt(110)
2n = sqrt(110)
n = sqrt(110)/2
n = sqrt(27.5)
n =~ 5.2440442408507577349572675683997

sqrt(110 - n) = n

110 - n = n^2

n^2 + n - 110 = 0

(n+11)(n-10) = 0

n = 10 & -11