36x^2-42x+12.25=0

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Solution for 36x^2-42x+12.25=0 equation:


Simplifying
36x2 + -42x + 12.25 = 0

Reorder the terms:
12.25 + -42x + 36x2 = 0

Solving
12.25 + -42x + 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'.
0.3402777778 + -1.166666667x + x2 = 0

Move the constant term to the right:

Add '-0.3402777778' to each side of the equation.
0.3402777778 + -1.166666667x + -0.3402777778 + x2 = 0 + -0.3402777778

Reorder the terms:
0.3402777778 + -0.3402777778 + -1.166666667x + x2 = 0 + -0.3402777778

Combine like terms: 0.3402777778 + -0.3402777778 = 0.0000000000
0.0000000000 + -1.166666667x + x2 = 0 + -0.3402777778
-1.166666667x + x2 = 0 + -0.3402777778

Combine like terms: 0 + -0.3402777778 = -0.3402777778
-1.166666667x + x2 = -0.3402777778

The x term is -1.166666667x.  Take half its coefficient (-0.5833333335).
Square it (0.3402777780) and add it to both sides.

Add '0.3402777780' to each side of the equation.
-1.166666667x + 0.3402777780 + x2 = -0.3402777778 + 0.3402777780

Reorder the terms:
0.3402777780 + -1.166666667x + x2 = -0.3402777778 + 0.3402777780

Combine like terms: -0.3402777778 + 0.3402777780 = 0.0000000002
0.3402777780 + -1.166666667x + x2 = 0.0000000002

Factor a perfect square on the left side:
(x + -0.5833333335)(x + -0.5833333335) = 0.0000000002

Calculate the square root of the right side: 0.000014142

Break this problem into two subproblems by setting 
(x + -0.5833333335) equal to 0.000014142 and -0.000014142.

Subproblem 1

x + -0.5833333335 = 0.000014142 Simplifying x + -0.5833333335 = 0.000014142 Reorder the terms: -0.5833333335 + x = 0.000014142 Solving -0.5833333335 + x = 0.000014142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + x = 0.000014142 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = 0.000014142 + 0.5833333335 x = 0.000014142 + 0.5833333335 Combine like terms: 0.000014142 + 0.5833333335 = 0.5833474755 x = 0.5833474755 Simplifying x = 0.5833474755

Subproblem 2

x + -0.5833333335 = -0.000014142 Simplifying x + -0.5833333335 = -0.000014142 Reorder the terms: -0.5833333335 + x = -0.000014142 Solving -0.5833333335 + x = -0.000014142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + x = -0.000014142 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = -0.000014142 + 0.5833333335 x = -0.000014142 + 0.5833333335 Combine like terms: -0.000014142 + 0.5833333335 = 0.5833191915 x = 0.5833191915 Simplifying x = 0.5833191915

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.5833474755, 0.5833191915}

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