(12x^2)-252x+902=0

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Solution for (12x^2)-252x+902=0 equation: 


Simplifying
(12x2) + -252x + 902 = 0

Reorder the terms:
902 + -252x + (12x2) = 0

Solving
902 + -252x + (12x2) = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(451 + -126x + (6x2)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(451 + -126x + (6x2))' equal to zero and attempt to solve:

Simplifying
451 + -126x + (6x2) = 0

Solving
451 + -126x + (6x2) = 0

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

Divide each side by '6'.
75.16666667 + -21x + x2 = 0

Move the constant term to the right:

Add '-75.16666667' to each side of the equation.
75.16666667 + -21x + -75.16666667 + x2 = 0 + -75.16666667

Reorder the terms:
75.16666667 + -75.16666667 + -21x + x2 = 0 + -75.16666667

Combine like terms: 75.16666667 + -75.16666667 = 0.00000000
0.00000000 + -21x + x2 = 0 + -75.16666667
-21x + x2 = 0 + -75.16666667

Combine like terms: 0 + -75.16666667 = -75.16666667
-21x + x2 = -75.16666667

The x term is -21x.  Take half its coefficient (-10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
-21x + 110.25 + x2 = -75.16666667 + 110.25

Reorder the terms:
110.25 + -21x + x2 = -75.16666667 + 110.25

Combine like terms: -75.16666667 + 110.25 = 35.08333333
110.25 + -21x + x2 = 35.08333333

Factor a perfect square on the left side:
((x) + -10.5)((x) + -10.5) = 35.08333333

Calculate the square root of the right side: 5.923118548

Break this problem into two subproblems by setting 
((x) + -10.5) equal to 5.923118548 and -5.923118548.


Subproblem 1
(x) + -10.5 = 5.923118548

Simplifying
(x) + -10.5 = 5.923118548
x + -10.5 = 5.923118548

Reorder the terms:
-10.5 + x = 5.923118548

Solving
-10.5 + x = 5.923118548

Solving for variable 'x'.

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

Add '10.5' to each side of the equation.
-10.5 + 10.5 + x = 5.923118548 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + x = 5.923118548 + 10.5
x = 5.923118548 + 10.5

Combine like terms: 5.923118548 + 10.5 = 16.423118548
x = 16.423118548

Simplifying
x = 16.423118548


Subproblem 2
(x) + -10.5 = -5.923118548

Simplifying
(x) + -10.5 = -5.923118548
x + -10.5 = -5.923118548

Reorder the terms:
-10.5 + x = -5.923118548

Solving
-10.5 + x = -5.923118548

Solving for variable 'x'.

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

Add '10.5' to each side of the equation.
-10.5 + 10.5 + x = -5.923118548 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + x = -5.923118548 + 10.5
x = -5.923118548 + 10.5

Combine like terms: -5.923118548 + 10.5 = 4.576881452
x = 4.576881452

Simplifying
x = 4.576881452


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.423118548, 4.576881452}
Solution
x = {16.423118548, 4.576881452}

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