36x^2+x-3=0

Solution for 36x^2+x-3=0 equation:

Simplifying
36x2 + x + -3 = 0

Reorder the terms:
-3 + x + 36x2 = 0

Solving
-3 + x + 36x2 = 0

Solving for variable 'x'.

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

Divide each side by '36'.
-0.08333333333 + 0.02777777778x + x2 = 0

Move the constant term to the right:

Add '0.08333333333' to each side of the equation.
-0.08333333333 + 0.02777777778x + 0.08333333333 + x2 = 0 + 0.08333333333

Reorder the terms:
-0.08333333333 + 0.08333333333 + 0.02777777778x + x2 = 0 + 0.08333333333

Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000
0.00000000000 + 0.02777777778x + x2 = 0 + 0.08333333333
0.02777777778x + x2 = 0 + 0.08333333333

Combine like terms: 0 + 0.08333333333 = 0.08333333333
0.02777777778x + x2 = 0.08333333333

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.02777777778x + 0.25 + x2 = 0.08333333333 + 0.25

Reorder the terms:
0.25 + 0.02777777778x + x2 = 0.08333333333 + 0.25

Combine like terms: 0.08333333333 + 0.25 = 0.33333333333
0.25 + 0.02777777778x + x2 = 0.33333333333

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.33333333333

Calculate the square root of the right side: 0.577350269

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.577350269 and -0.577350269.

Subproblem 1
x + 0.5 = 0.577350269

Simplifying
x + 0.5 = 0.577350269

Reorder the terms:
0.5 + x = 0.577350269

Solving
0.5 + x = 0.577350269

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 0.577350269 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0.577350269 + -0.5
x = 0.577350269 + -0.5

Combine like terms: 0.577350269 + -0.5 = 0.077350269
x = 0.077350269

Simplifying
x = 0.077350269

Subproblem 2
x + 0.5 = -0.577350269

Simplifying
x + 0.5 = -0.577350269

Reorder the terms:
0.5 + x = -0.577350269

Solving
0.5 + x = -0.577350269

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -0.577350269 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -0.577350269 + -0.5
x = -0.577350269 + -0.5

Combine like terms: -0.577350269 + -0.5 = -1.077350269
x = -1.077350269

Simplifying
x = -1.077350269

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.077350269, -1.077350269}