12x^2-30x+2=0

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Solution for 12x^2-30x+2=0 equation: 


Simplifying
12x2 + -30x + 2 = 0

Reorder the terms:
2 + -30x + 12x2 = 0

Solving
2 + -30x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -15x + 6x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + -15x + 6x2)' equal to zero and attempt to solve:

Simplifying
1 + -15x + 6x2 = 0

Solving
1 + -15x + 6x2 = 0

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

Divide each side by '6'.
0.1666666667 + -2.5x + x2 = 0

Move the constant term to the right:

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -2.5x + -0.1666666667 + x2 = 0 + -0.1666666667

Reorder the terms:
0.1666666667 + -0.1666666667 + -2.5x + x2 = 0 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + -2.5x + x2 = 0 + -0.1666666667
-2.5x + x2 = 0 + -0.1666666667

Combine like terms: 0 + -0.1666666667 = -0.1666666667
-2.5x + x2 = -0.1666666667

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = -0.1666666667 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = -0.1666666667 + 1.5625

Combine like terms: -0.1666666667 + 1.5625 = 1.3958333333
1.5625 + -2.5x + x2 = 1.3958333333

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 1.3958333333

Calculate the square root of the right side: 1.181453907

Break this problem into two subproblems by setting 
(x + -1.25) equal to 1.181453907 and -1.181453907.


Subproblem 1
x + -1.25 = 1.181453907

Simplifying
x + -1.25 = 1.181453907

Reorder the terms:
-1.25 + x = 1.181453907

Solving
-1.25 + x = 1.181453907

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = 1.181453907 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = 1.181453907 + 1.25
x = 1.181453907 + 1.25

Combine like terms: 1.181453907 + 1.25 = 2.431453907
x = 2.431453907

Simplifying
x = 2.431453907


Subproblem 2
x + -1.25 = -1.181453907

Simplifying
x + -1.25 = -1.181453907

Reorder the terms:
-1.25 + x = -1.181453907

Solving
-1.25 + x = -1.181453907

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = -1.181453907 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = -1.181453907 + 1.25
x = -1.181453907 + 1.25

Combine like terms: -1.181453907 + 1.25 = 0.068546093
x = 0.068546093

Simplifying
x = 0.068546093


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.431453907, 0.068546093}
Solution
x = {2.431453907, 0.068546093}

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