12x^2-148x+405=0

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Solution for 12x^2-148x+405=0 equation: 


Simplifying
12x2 + -148x + 405 = 0

Reorder the terms:
405 + -148x + 12x2 = 0

Solving
405 + -148x + 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'.
33.75 + -12.33333333x + x2 = 0

Move the constant term to the right:

Add '-33.75' to each side of the equation.
33.75 + -12.33333333x + -33.75 + x2 = 0 + -33.75

Reorder the terms:
33.75 + -33.75 + -12.33333333x + x2 = 0 + -33.75

Combine like terms: 33.75 + -33.75 = 0.00
0.00 + -12.33333333x + x2 = 0 + -33.75
-12.33333333x + x2 = 0 + -33.75

Combine like terms: 0 + -33.75 = -33.75
-12.33333333x + x2 = -33.75

The x term is -12.33333333x.  Take half its coefficient (-6.166666665).
Square it (38.02777776) and add it to both sides.

Add '38.02777776' to each side of the equation.
-12.33333333x + 38.02777776 + x2 = -33.75 + 38.02777776

Reorder the terms:
38.02777776 + -12.33333333x + x2 = -33.75 + 38.02777776

Combine like terms: -33.75 + 38.02777776 = 4.27777776
38.02777776 + -12.33333333x + x2 = 4.27777776

Factor a perfect square on the left side:
(x + -6.166666665)(x + -6.166666665) = 4.27777776

Calculate the square root of the right side: 2.068278937

Break this problem into two subproblems by setting 
(x + -6.166666665) equal to 2.068278937 and -2.068278937.


Subproblem 1
x + -6.166666665 = 2.068278937

Simplifying
x + -6.166666665 = 2.068278937

Reorder the terms:
-6.166666665 + x = 2.068278937

Solving
-6.166666665 + x = 2.068278937

Solving for variable 'x'.

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

Add '6.166666665' to each side of the equation.
-6.166666665 + 6.166666665 + x = 2.068278937 + 6.166666665

Combine like terms: -6.166666665 + 6.166666665 = 0.000000000
0.000000000 + x = 2.068278937 + 6.166666665
x = 2.068278937 + 6.166666665

Combine like terms: 2.068278937 + 6.166666665 = 8.234945602
x = 8.234945602

Simplifying
x = 8.234945602


Subproblem 2
x + -6.166666665 = -2.068278937

Simplifying
x + -6.166666665 = -2.068278937

Reorder the terms:
-6.166666665 + x = -2.068278937

Solving
-6.166666665 + x = -2.068278937

Solving for variable 'x'.

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

Add '6.166666665' to each side of the equation.
-6.166666665 + 6.166666665 + x = -2.068278937 + 6.166666665

Combine like terms: -6.166666665 + 6.166666665 = 0.000000000
0.000000000 + x = -2.068278937 + 6.166666665
x = -2.068278937 + 6.166666665

Combine like terms: -2.068278937 + 6.166666665 = 4.098387728
x = 4.098387728

Simplifying
x = 4.098387728


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.234945602, 4.098387728}

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