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3 Answers

Do you mean square root of(11-x) ?
If so, [square root(11-x)]^2=(x+1)^2
11-x=x^2+2x+1
11=x^2+3x+1
0=x^2+3x-10
x^2+3x-10=0
(x+5)(x-2)=0
x+5=0, x=-5
x-2=0, x=2
check: SQRT(11-(-5))=SQRT(16)=4 and x+1=-5+1=-4 but SQRT symbol means principal root
(the nonnegative root)
we don't use -5 as a solution
SQRT(11-2)=SQRT(9)=3 and x+1=2+1=3
we use x=2 as a solution

Comments

Given the number of "creative" ways in which some of the questions arrive, I am inclined to your interpretation.
Michael F.
The problem is, Michael, that the square root symbol appears to omit the top horizontal line over the radicand.
Arthur D.
(11)½ - x = x + 1
 
Add x to each side of the equation:
 
(11)½ = 2x + 1
 
Subtract 1 from each side of the equation:
 
(11)½ - 1 = 2x
 
2x = (11)½ - 1 = 3.317 - 1 = 2.317
 
∴x = 1.158