12x^2-36x+25=0

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Solution for 12x^2-36x+25=0 equation:


Simplifying
12x2 + -36x + 25 = 0

Reorder the terms:
25 + -36x + 12x2 = 0

Solving
25 + -36x + 12x2 = 0

Solving for variable 'x'.

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

Divide each side by '12'.
2.083333333 + -3x + x2 = 0

Move the constant term to the right:

Add '-2.083333333' to each side of the equation.
2.083333333 + -3x + -2.083333333 + x2 = 0 + -2.083333333

Reorder the terms:
2.083333333 + -2.083333333 + -3x + x2 = 0 + -2.083333333

Combine like terms: 2.083333333 + -2.083333333 = 0.000000000
0.000000000 + -3x + x2 = 0 + -2.083333333
-3x + x2 = 0 + -2.083333333

Combine like terms: 0 + -2.083333333 = -2.083333333
-3x + x2 = -2.083333333

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = -2.083333333 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -2.083333333 + 2.25

Combine like terms: -2.083333333 + 2.25 = 0.166666667
2.25 + -3x + x2 = 0.166666667

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 0.166666667

Calculate the square root of the right side: 0.408248291

Break this problem into two subproblems by setting 
(x + -1.5) equal to 0.408248291 and -0.408248291.

Subproblem 1

x + -1.5 = 0.408248291 Simplifying x + -1.5 = 0.408248291 Reorder the terms: -1.5 + x = 0.408248291 Solving -1.5 + x = 0.408248291 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 0.408248291 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 0.408248291 + 1.5 x = 0.408248291 + 1.5 Combine like terms: 0.408248291 + 1.5 = 1.908248291 x = 1.908248291 Simplifying x = 1.908248291

Subproblem 2

x + -1.5 = -0.408248291 Simplifying x + -1.5 = -0.408248291 Reorder the terms: -1.5 + x = -0.408248291 Solving -1.5 + x = -0.408248291 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -0.408248291 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -0.408248291 + 1.5 x = -0.408248291 + 1.5 Combine like terms: -0.408248291 + 1.5 = 1.091751709 x = 1.091751709 Simplifying x = 1.091751709

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.908248291, 1.091751709}

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