2r^2-4r+11=0

Solution for 2r^2-4r+11=0 equation:

Simplifying
2r2 + -4r + 11 = 0

Reorder the terms:
11 + -4r + 2r2 = 0

Solving
11 + -4r + 2r2 = 0

Solving for variable 'r'.

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
5.5 + -2r + r2 = 0

Move the constant term to the right:

Add '-5.5' to each side of the equation.
5.5 + -2r + -5.5 + r2 = 0 + -5.5

Reorder the terms:
5.5 + -5.5 + -2r + r2 = 0 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + -2r + r2 = 0 + -5.5
-2r + r2 = 0 + -5.5

Combine like terms: 0 + -5.5 = -5.5
-2r + r2 = -5.5

The r term is -2r.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2r + 1 + r2 = -5.5 + 1

Reorder the terms:
1 + -2r + r2 = -5.5 + 1

Combine like terms: -5.5 + 1 = -4.5
1 + -2r + r2 = -4.5

Factor a perfect square on the left side:
(r + -1)(r + -1) = -4.5

Can't calculate square root of the right side.

The solution to this equation could not be determined.