6x^2+23x-36=0

Solution for 6x^2+23x-36=0 equation:

Simplifying
6x2 + 23x + -36 = 0

Reorder the terms:
-36 + 23x + 6x2 = 0

Solving
-36 + 23x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
-6 + 3.833333333x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 3.833333333x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + 3.833333333x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 3.833333333x + x2 = 0 + 6
3.833333333x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
3.833333333x + x2 = 6

The x term is 3.833333333x.  Take half its coefficient (1.916666667).
Square it (3.673611112) and add it to both sides.

Add '3.673611112' to each side of the equation.
3.833333333x + 3.673611112 + x2 = 6 + 3.673611112

Reorder the terms:
3.673611112 + 3.833333333x + x2 = 6 + 3.673611112

Combine like terms: 6 + 3.673611112 = 9.673611112
3.673611112 + 3.833333333x + x2 = 9.673611112

Factor a perfect square on the left side:
(x + 1.916666667)(x + 1.916666667) = 9.673611112

Calculate the square root of the right side: 3.110242935

Break this problem into two subproblems by setting 
(x + 1.916666667) equal to 3.110242935 and -3.110242935.

Subproblem 1
x + 1.916666667 = 3.110242935

Simplifying
x + 1.916666667 = 3.110242935

Reorder the terms:
1.916666667 + x = 3.110242935

Solving
1.916666667 + x = 3.110242935

Solving for variable 'x'.

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

Add '-1.916666667' to each side of the equation.
1.916666667 + -1.916666667 + x = 3.110242935 + -1.916666667

Combine like terms: 1.916666667 + -1.916666667 = 0.000000000
0.000000000 + x = 3.110242935 + -1.916666667
x = 3.110242935 + -1.916666667

Combine like terms: 3.110242935 + -1.916666667 = 1.193576268
x = 1.193576268

Simplifying
x = 1.193576268

Subproblem 2
x + 1.916666667 = -3.110242935

Simplifying
x + 1.916666667 = -3.110242935

Reorder the terms:
1.916666667 + x = -3.110242935

Solving
1.916666667 + x = -3.110242935

Solving for variable 'x'.

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

Add '-1.916666667' to each side of the equation.
1.916666667 + -1.916666667 + x = -3.110242935 + -1.916666667

Combine like terms: 1.916666667 + -1.916666667 = 0.000000000
0.000000000 + x = -3.110242935 + -1.916666667
x = -3.110242935 + -1.916666667

Combine like terms: -3.110242935 + -1.916666667 = -5.026909602
x = -5.026909602

Simplifying
x = -5.026909602

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.193576268, -5.026909602}