12X^2-84X+110=0

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Solution for 12X^2-84X+110=0 equation: 


Simplifying
12X2 + -84X + 110 = 0

Reorder the terms:
110 + -84X + 12X2 = 0

Solving
110 + -84X + 12X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '2'.
2(55 + -42X + 6X2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(55 + -42X + 6X2)' equal to zero and attempt to solve:

Simplifying
55 + -42X + 6X2 = 0

Solving
55 + -42X + 6X2 = 0

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

Divide each side by '6'.
9.166666667 + -7X + X2 = 0

Move the constant term to the right:

Add '-9.166666667' to each side of the equation.
9.166666667 + -7X + -9.166666667 + X2 = 0 + -9.166666667

Reorder the terms:
9.166666667 + -9.166666667 + -7X + X2 = 0 + -9.166666667

Combine like terms: 9.166666667 + -9.166666667 = 0.000000000
0.000000000 + -7X + X2 = 0 + -9.166666667
-7X + X2 = 0 + -9.166666667

Combine like terms: 0 + -9.166666667 = -9.166666667
-7X + X2 = -9.166666667

The X term is -7X.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7X + 12.25 + X2 = -9.166666667 + 12.25

Reorder the terms:
12.25 + -7X + X2 = -9.166666667 + 12.25

Combine like terms: -9.166666667 + 12.25 = 3.083333333
12.25 + -7X + X2 = 3.083333333

Factor a perfect square on the left side:
(X + -3.5)(X + -3.5) = 3.083333333

Calculate the square root of the right side: 1.755942292

Break this problem into two subproblems by setting 
(X + -3.5) equal to 1.755942292 and -1.755942292.


Subproblem 1
X + -3.5 = 1.755942292

Simplifying
X + -3.5 = 1.755942292

Reorder the terms:
-3.5 + X = 1.755942292

Solving
-3.5 + X = 1.755942292

Solving for variable 'X'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + X = 1.755942292 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + X = 1.755942292 + 3.5
X = 1.755942292 + 3.5

Combine like terms: 1.755942292 + 3.5 = 5.255942292
X = 5.255942292

Simplifying
X = 5.255942292


Subproblem 2
X + -3.5 = -1.755942292

Simplifying
X + -3.5 = -1.755942292

Reorder the terms:
-3.5 + X = -1.755942292

Solving
-3.5 + X = -1.755942292

Solving for variable 'X'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + X = -1.755942292 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + X = -1.755942292 + 3.5
X = -1.755942292 + 3.5

Combine like terms: -1.755942292 + 3.5 = 1.744057708
X = 1.744057708

Simplifying
X = 1.744057708


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {5.255942292, 1.744057708}
Solution
X = {5.255942292, 1.744057708}

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