0.11x^2+0.3x-5=0

Solution for 0.11x^2+0.3x-5=0 equation:

Simplifying
0.11x2 + 0.3x + -5 = 0

Reorder the terms:
-5 + 0.3x + 0.11x2 = 0

Solving
-5 + 0.3x + 0.11x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.11'.
-45.45454545 + 2.727272727x + x2 = 0

Move the constant term to the right:

Add '45.45454545' to each side of the equation.
-45.45454545 + 2.727272727x + 45.45454545 + x2 = 0 + 45.45454545

Reorder the terms:
-45.45454545 + 45.45454545 + 2.727272727x + x2 = 0 + 45.45454545

Combine like terms: -45.45454545 + 45.45454545 = 0.00000000
0.00000000 + 2.727272727x + x2 = 0 + 45.45454545
2.727272727x + x2 = 0 + 45.45454545

Combine like terms: 0 + 45.45454545 = 45.45454545
2.727272727x + x2 = 45.45454545

The x term is 2.727272727x.  Take half its coefficient (1.363636364).
Square it (1.859504133) and add it to both sides.

Add '1.859504133' to each side of the equation.
2.727272727x + 1.859504133 + x2 = 45.45454545 + 1.859504133

Reorder the terms:
1.859504133 + 2.727272727x + x2 = 45.45454545 + 1.859504133

Combine like terms: 45.45454545 + 1.859504133 = 47.314049583
1.859504133 + 2.727272727x + x2 = 47.314049583

Factor a perfect square on the left side:
(x + 1.363636364)(x + 1.363636364) = 47.314049583

Calculate the square root of the right side: 6.878520886

Break this problem into two subproblems by setting 
(x + 1.363636364) equal to 6.878520886 and -6.878520886.

Subproblem 1
x + 1.363636364 = 6.878520886

Simplifying
x + 1.363636364 = 6.878520886

Reorder the terms:
1.363636364 + x = 6.878520886

Solving
1.363636364 + x = 6.878520886

Solving for variable 'x'.

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

Add '-1.363636364' to each side of the equation.
1.363636364 + -1.363636364 + x = 6.878520886 + -1.363636364

Combine like terms: 1.363636364 + -1.363636364 = 0.000000000
0.000000000 + x = 6.878520886 + -1.363636364
x = 6.878520886 + -1.363636364

Combine like terms: 6.878520886 + -1.363636364 = 5.514884522
x = 5.514884522

Simplifying
x = 5.514884522

Subproblem 2
x + 1.363636364 = -6.878520886

Simplifying
x + 1.363636364 = -6.878520886

Reorder the terms:
1.363636364 + x = -6.878520886

Solving
1.363636364 + x = -6.878520886

Solving for variable 'x'.

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

Add '-1.363636364' to each side of the equation.
1.363636364 + -1.363636364 + x = -6.878520886 + -1.363636364

Combine like terms: 1.363636364 + -1.363636364 = 0.000000000
0.000000000 + x = -6.878520886 + -1.363636364
x = -6.878520886 + -1.363636364

Combine like terms: -6.878520886 + -1.363636364 = -8.24215725
x = -8.24215725

Simplifying
x = -8.24215725

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.514884522, -8.24215725}