x^2+35.4x-1296=0

Solution for x^2+35.4x-1296=0 equation:

Simplifying
x2 + 35.4x + -1296 = 0

Reorder the terms:
-1296 + 35.4x + x2 = 0

Solving
-1296 + 35.4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1296' to each side of the equation.
-1296 + 35.4x + 1296 + x2 = 0 + 1296

Reorder the terms:
-1296 + 1296 + 35.4x + x2 = 0 + 1296

Combine like terms: -1296 + 1296 = 0
0 + 35.4x + x2 = 0 + 1296
35.4x + x2 = 0 + 1296

Combine like terms: 0 + 1296 = 1296
35.4x + x2 = 1296

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 = 1296 + 313.29

Reorder the terms:
313.29 + 35.4x + x2 = 1296 + 313.29

Combine like terms: 1296 + 313.29 = 1609.29
313.29 + 35.4x + x2 = 1609.29

Factor a perfect square on the left side:
(x + 17.7)(x + 17.7) = 1609.29

Calculate the square root of the right side: 40.115956925

Break this problem into two subproblems by setting 
(x + 17.7) equal to 40.115956925 and -40.115956925.

Subproblem 1
x + 17.7 = 40.115956925

Simplifying
x + 17.7 = 40.115956925

Reorder the terms:
17.7 + x = 40.115956925

Solving
17.7 + x = 40.115956925

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 = 40.115956925 + -17.7

Combine like terms: 17.7 + -17.7 = 0.0
0.0 + x = 40.115956925 + -17.7
x = 40.115956925 + -17.7

Combine like terms: 40.115956925 + -17.7 = 22.415956925
x = 22.415956925

Simplifying
x = 22.415956925

Subproblem 2
x + 17.7 = -40.115956925

Simplifying
x + 17.7 = -40.115956925

Reorder the terms:
17.7 + x = -40.115956925

Solving
17.7 + x = -40.115956925

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 = -40.115956925 + -17.7

Combine like terms: 17.7 + -17.7 = 0.0
0.0 + x = -40.115956925 + -17.7
x = -40.115956925 + -17.7

Combine like terms: -40.115956925 + -17.7 = -57.815956925
x = -57.815956925

Simplifying
x = -57.815956925

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.415956925, -57.815956925}