11x^2-36x+27=0

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Solution for 11x^2-36x+27=0 equation:


Simplifying
11x2 + -36x + 27 = 0

Reorder the terms:
27 + -36x + 11x2 = 0

Solving
27 + -36x + 11x2 = 0

Solving for variable 'x'.

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

Divide each side by '11'.
2.454545455 + -3.272727273x + x2 = 0

Move the constant term to the right:

Add '-2.454545455' to each side of the equation.
2.454545455 + -3.272727273x + -2.454545455 + x2 = 0 + -2.454545455

Reorder the terms:
2.454545455 + -2.454545455 + -3.272727273x + x2 = 0 + -2.454545455

Combine like terms: 2.454545455 + -2.454545455 = 0.000000000
0.000000000 + -3.272727273x + x2 = 0 + -2.454545455
-3.272727273x + x2 = 0 + -2.454545455

Combine like terms: 0 + -2.454545455 = -2.454545455
-3.272727273x + x2 = -2.454545455

The x term is -3.272727273x.  Take half its coefficient (-1.636363637).
Square it (2.677685953) and add it to both sides.

Add '2.677685953' to each side of the equation.
-3.272727273x + 2.677685953 + x2 = -2.454545455 + 2.677685953

Reorder the terms:
2.677685953 + -3.272727273x + x2 = -2.454545455 + 2.677685953

Combine like terms: -2.454545455 + 2.677685953 = 0.223140498
2.677685953 + -3.272727273x + x2 = 0.223140498

Factor a perfect square on the left side:
(x + -1.636363637)(x + -1.636363637) = 0.223140498

Calculate the square root of the right side: 0.472377495

Break this problem into two subproblems by setting 
(x + -1.636363637) equal to 0.472377495 and -0.472377495.

Subproblem 1

x + -1.636363637 = 0.472377495 Simplifying x + -1.636363637 = 0.472377495 Reorder the terms: -1.636363637 + x = 0.472377495 Solving -1.636363637 + x = 0.472377495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.636363637' to each side of the equation. -1.636363637 + 1.636363637 + x = 0.472377495 + 1.636363637 Combine like terms: -1.636363637 + 1.636363637 = 0.000000000 0.000000000 + x = 0.472377495 + 1.636363637 x = 0.472377495 + 1.636363637 Combine like terms: 0.472377495 + 1.636363637 = 2.108741132 x = 2.108741132 Simplifying x = 2.108741132

Subproblem 2

x + -1.636363637 = -0.472377495 Simplifying x + -1.636363637 = -0.472377495 Reorder the terms: -1.636363637 + x = -0.472377495 Solving -1.636363637 + x = -0.472377495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.636363637' to each side of the equation. -1.636363637 + 1.636363637 + x = -0.472377495 + 1.636363637 Combine like terms: -1.636363637 + 1.636363637 = 0.000000000 0.000000000 + x = -0.472377495 + 1.636363637 x = -0.472377495 + 1.636363637 Combine like terms: -0.472377495 + 1.636363637 = 1.163986142 x = 1.163986142 Simplifying x = 1.163986142

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.108741132, 1.163986142}

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