5m^2-3-11m=0

Solution for 5m^2-3-11m=0 equation:

Simplifying
5m2 + -3 + -11m = 0

Reorder the terms:
-3 + -11m + 5m2 = 0

Solving
-3 + -11m + 5m2 = 0

Solving for variable 'm'.

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

Divide each side by '5'.
-0.6 + -2.2m + m2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + -2.2m + 0.6 + m2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + -2.2m + m2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + -2.2m + m2 = 0 + 0.6
-2.2m + m2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
-2.2m + m2 = 0.6

The m term is -2.2m.  Take half its coefficient (-1.1).
Square it (1.21) and add it to both sides.

Add '1.21' to each side of the equation.
-2.2m + 1.21 + m2 = 0.6 + 1.21

Reorder the terms:
1.21 + -2.2m + m2 = 0.6 + 1.21

Combine like terms: 0.6 + 1.21 = 1.81
1.21 + -2.2m + m2 = 1.81

Factor a perfect square on the left side:
(m + -1.1)(m + -1.1) = 1.81

Calculate the square root of the right side: 1.345362405

Break this problem into two subproblems by setting 
(m + -1.1) equal to 1.345362405 and -1.345362405.

Subproblem 1
m + -1.1 = 1.345362405

Simplifying
m + -1.1 = 1.345362405

Reorder the terms:
-1.1 + m = 1.345362405

Solving
-1.1 + m = 1.345362405

Solving for variable 'm'.

Move all terms containing m to the left, all other terms to the right.

Add '1.1' to each side of the equation.
-1.1 + 1.1 + m = 1.345362405 + 1.1

Combine like terms: -1.1 + 1.1 = 0.0
0.0 + m = 1.345362405 + 1.1
m = 1.345362405 + 1.1

Combine like terms: 1.345362405 + 1.1 = 2.445362405
m = 2.445362405

Simplifying
m = 2.445362405

Subproblem 2
m + -1.1 = -1.345362405

Simplifying
m + -1.1 = -1.345362405

Reorder the terms:
-1.1 + m = -1.345362405

Solving
-1.1 + m = -1.345362405

Solving for variable 'm'.

Move all terms containing m to the left, all other terms to the right.

Add '1.1' to each side of the equation.
-1.1 + 1.1 + m = -1.345362405 + 1.1

Combine like terms: -1.1 + 1.1 = 0.0
0.0 + m = -1.345362405 + 1.1
m = -1.345362405 + 1.1

Combine like terms: -1.345362405 + 1.1 = -0.245362405
m = -0.245362405

Simplifying
m = -0.245362405

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {2.445362405, -0.245362405}