6x^2+11x-36=0

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Solution for 6x^2+11x-36=0 equation:


Simplifying
6x2 + 11x + -36 = 0

Reorder the terms:
-36 + 11x + 6x2 = 0

Solving
-36 + 11x + 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 + 1.833333333x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 1.833333333x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + 1.833333333x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 1.833333333x + x2 = 0 + 6
1.833333333x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
1.833333333x + x2 = 6

The x term is 1.833333333x.  Take half its coefficient (0.9166666665).
Square it (0.8402777775) and add it to both sides.

Add '0.8402777775' to each side of the equation.
1.833333333x + 0.8402777775 + x2 = 6 + 0.8402777775

Reorder the terms:
0.8402777775 + 1.833333333x + x2 = 6 + 0.8402777775

Combine like terms: 6 + 0.8402777775 = 6.8402777775
0.8402777775 + 1.833333333x + x2 = 6.8402777775

Factor a perfect square on the left side:
(x + 0.9166666665)(x + 0.9166666665) = 6.8402777775

Calculate the square root of the right side: 2.615392471

Break this problem into two subproblems by setting 
(x + 0.9166666665) equal to 2.615392471 and -2.615392471.

Subproblem 1

x + 0.9166666665 = 2.615392471 Simplifying x + 0.9166666665 = 2.615392471 Reorder the terms: 0.9166666665 + x = 2.615392471 Solving 0.9166666665 + x = 2.615392471 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9166666665' to each side of the equation. 0.9166666665 + -0.9166666665 + x = 2.615392471 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + x = 2.615392471 + -0.9166666665 x = 2.615392471 + -0.9166666665 Combine like terms: 2.615392471 + -0.9166666665 = 1.6987258045 x = 1.6987258045 Simplifying x = 1.6987258045

Subproblem 2

x + 0.9166666665 = -2.615392471 Simplifying x + 0.9166666665 = -2.615392471 Reorder the terms: 0.9166666665 + x = -2.615392471 Solving 0.9166666665 + x = -2.615392471 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9166666665' to each side of the equation. 0.9166666665 + -0.9166666665 + x = -2.615392471 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + x = -2.615392471 + -0.9166666665 x = -2.615392471 + -0.9166666665 Combine like terms: -2.615392471 + -0.9166666665 = -3.5320591375 x = -3.5320591375 Simplifying x = -3.5320591375

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.6987258045, -3.5320591375}

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