3x^2-36x+13=0

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Solution for 3x^2-36x+13=0 equation:


Simplifying
3x2 + -36x + 13 = 0

Reorder the terms:
13 + -36x + 3x2 = 0

Solving
13 + -36x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
4.333333333 + -12x + x2 = 0

Move the constant term to the right:

Add '-4.333333333' to each side of the equation.
4.333333333 + -12x + -4.333333333 + x2 = 0 + -4.333333333

Reorder the terms:
4.333333333 + -4.333333333 + -12x + x2 = 0 + -4.333333333

Combine like terms: 4.333333333 + -4.333333333 = 0.000000000
0.000000000 + -12x + x2 = 0 + -4.333333333
-12x + x2 = 0 + -4.333333333

Combine like terms: 0 + -4.333333333 = -4.333333333
-12x + x2 = -4.333333333

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = -4.333333333 + 36

Reorder the terms:
36 + -12x + x2 = -4.333333333 + 36

Combine like terms: -4.333333333 + 36 = 31.666666667
36 + -12x + x2 = 31.666666667

Factor a perfect square on the left side:
(x + -6)(x + -6) = 31.666666667

Calculate the square root of the right side: 5.627314339

Break this problem into two subproblems by setting 
(x + -6) equal to 5.627314339 and -5.627314339.

Subproblem 1

x + -6 = 5.627314339 Simplifying x + -6 = 5.627314339 Reorder the terms: -6 + x = 5.627314339 Solving -6 + x = 5.627314339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 5.627314339 + 6 Combine like terms: -6 + 6 = 0 0 + x = 5.627314339 + 6 x = 5.627314339 + 6 Combine like terms: 5.627314339 + 6 = 11.627314339 x = 11.627314339 Simplifying x = 11.627314339

Subproblem 2

x + -6 = -5.627314339 Simplifying x + -6 = -5.627314339 Reorder the terms: -6 + x = -5.627314339 Solving -6 + x = -5.627314339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -5.627314339 + 6 Combine like terms: -6 + 6 = 0 0 + x = -5.627314339 + 6 x = -5.627314339 + 6 Combine like terms: -5.627314339 + 6 = 0.372685661 x = 0.372685661 Simplifying x = 0.372685661

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.627314339, 0.372685661}

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