x^2+11.8x-40.88=0

Solution for x^2+11.8x-40.88=0 equation:

Simplifying
x2 + 11.8x + -40.88 = 0

Reorder the terms:
-40.88 + 11.8x + x2 = 0

Solving
-40.88 + 11.8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '40.88' to each side of the equation.
-40.88 + 11.8x + 40.88 + x2 = 0 + 40.88

Reorder the terms:
-40.88 + 40.88 + 11.8x + x2 = 0 + 40.88

Combine like terms: -40.88 + 40.88 = 0.00
0.00 + 11.8x + x2 = 0 + 40.88
11.8x + x2 = 0 + 40.88

Combine like terms: 0 + 40.88 = 40.88
11.8x + x2 = 40.88

The x term is 11.8x.  Take half its coefficient (5.9).
Square it (34.81) and add it to both sides.

Add '34.81' to each side of the equation.
11.8x + 34.81 + x2 = 40.88 + 34.81

Reorder the terms:
34.81 + 11.8x + x2 = 40.88 + 34.81

Combine like terms: 40.88 + 34.81 = 75.69
34.81 + 11.8x + x2 = 75.69

Factor a perfect square on the left side:
(x + 5.9)(x + 5.9) = 75.69

Calculate the square root of the right side: 8.7

Break this problem into two subproblems by setting 
(x + 5.9) equal to 8.7 and -8.7.

Subproblem 1
x + 5.9 = 8.7

Simplifying
x + 5.9 = 8.7

Reorder the terms:
5.9 + x = 8.7

Solving
5.9 + x = 8.7

Solving for variable 'x'.

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

Add '-5.9' to each side of the equation.
5.9 + -5.9 + x = 8.7 + -5.9

Combine like terms: 5.9 + -5.9 = 0.0
0.0 + x = 8.7 + -5.9
x = 8.7 + -5.9

Combine like terms: 8.7 + -5.9 = 2.8
x = 2.8

Simplifying
x = 2.8

Subproblem 2
x + 5.9 = -8.7

Simplifying
x + 5.9 = -8.7

Reorder the terms:
5.9 + x = -8.7

Solving
5.9 + x = -8.7

Solving for variable 'x'.

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

Add '-5.9' to each side of the equation.
5.9 + -5.9 + x = -8.7 + -5.9

Combine like terms: 5.9 + -5.9 = 0.0
0.0 + x = -8.7 + -5.9
x = -8.7 + -5.9

Combine like terms: -8.7 + -5.9 = -14.6
x = -14.6

Simplifying
x = -14.6

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.8, -14.6}