x^2+35.4x-55.55=0

Solution for x^2+35.4x-55.55=0 equation:

Simplifying
x2 + 35.4x + -55.55 = 0

Reorder the terms:
-55.55 + 35.4x + x2 = 0

Solving
-55.55 + 35.4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '55.55' to each side of the equation.
-55.55 + 35.4x + 55.55 + x2 = 0 + 55.55

Reorder the terms:
-55.55 + 55.55 + 35.4x + x2 = 0 + 55.55

Combine like terms: -55.55 + 55.55 = 0.00
0.00 + 35.4x + x2 = 0 + 55.55
35.4x + x2 = 0 + 55.55

Combine like terms: 0 + 55.55 = 55.55
35.4x + x2 = 55.55

The x term is 35.4x.  Take half its coefficient (17.7).
Square it (313.29) and add it to both sides.

Add '313.29' to each side of the equation.
35.4x + 313.29 + x2 = 55.55 + 313.29

Reorder the terms:
313.29 + 35.4x + x2 = 55.55 + 313.29

Combine like terms: 55.55 + 313.29 = 368.84
313.29 + 35.4x + x2 = 368.84

Factor a perfect square on the left side:
(x + 17.7)(x + 17.7) = 368.84

Calculate the square root of the right side: 19.205207627

Break this problem into two subproblems by setting 
(x + 17.7) equal to 19.205207627 and -19.205207627.

Subproblem 1
x + 17.7 = 19.205207627

Simplifying
x + 17.7 = 19.205207627

Reorder the terms:
17.7 + x = 19.205207627

Solving
17.7 + x = 19.205207627

Solving for variable 'x'.

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

Add '-17.7' to each side of the equation.
17.7 + -17.7 + x = 19.205207627 + -17.7

Combine like terms: 17.7 + -17.7 = 0.0
0.0 + x = 19.205207627 + -17.7
x = 19.205207627 + -17.7

Combine like terms: 19.205207627 + -17.7 = 1.505207627
x = 1.505207627

Simplifying
x = 1.505207627

Subproblem 2
x + 17.7 = -19.205207627

Simplifying
x + 17.7 = -19.205207627

Reorder the terms:
17.7 + x = -19.205207627

Solving
17.7 + x = -19.205207627

Solving for variable 'x'.

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

Add '-17.7' to each side of the equation.
17.7 + -17.7 + x = -19.205207627 + -17.7

Combine like terms: 17.7 + -17.7 = 0.0
0.0 + x = -19.205207627 + -17.7
x = -19.205207627 + -17.7

Combine like terms: -19.205207627 + -17.7 = -36.905207627
x = -36.905207627

Simplifying
x = -36.905207627

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.505207627, -36.905207627}