12x^2+98x+108=0

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Solution for 12x^2+98x+108=0 equation:


Simplifying
12x2 + 98x + 108 = 0

Reorder the terms:
108 + 98x + 12x2 = 0

Solving
108 + 98x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(54 + 49x + 6x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(54 + 49x + 6x2)' equal to zero and attempt to solve:

Simplifying
54 + 49x + 6x2 = 0

Solving
54 + 49x + 6x2 = 0

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

Divide each side by '6'.
9 + 8.166666667x + x2 = 0

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + 8.166666667x + -9 + x2 = 0 + -9

Reorder the terms:
9 + -9 + 8.166666667x + x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 8.166666667x + x2 = 0 + -9
8.166666667x + x2 = 0 + -9

Combine like terms: 0 + -9 = -9
8.166666667x + x2 = -9

The x term is 8.166666667x.  Take half its coefficient (4.083333334).
Square it (16.67361112) and add it to both sides.

Add '16.67361112' to each side of the equation.
8.166666667x + 16.67361112 + x2 = -9 + 16.67361112

Reorder the terms:
16.67361112 + 8.166666667x + x2 = -9 + 16.67361112

Combine like terms: -9 + 16.67361112 = 7.67361112
16.67361112 + 8.166666667x + x2 = 7.67361112

Factor a perfect square on the left side:
(x + 4.083333334)(x + 4.083333334) = 7.67361112

Calculate the square root of the right side: 2.770128358

Break this problem into two subproblems by setting 
(x + 4.083333334) equal to 2.770128358 and -2.770128358.


Subproblem 1
x + 4.083333334 = 2.770128358

Simplifying
x + 4.083333334 = 2.770128358

Reorder the terms:
4.083333334 + x = 2.770128358

Solving
4.083333334 + x = 2.770128358

Solving for variable 'x'.

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

Add '-4.083333334' to each side of the equation.
4.083333334 + -4.083333334 + x = 2.770128358 + -4.083333334

Combine like terms: 4.083333334 + -4.083333334 = 0.000000000
0.000000000 + x = 2.770128358 + -4.083333334
x = 2.770128358 + -4.083333334

Combine like terms: 2.770128358 + -4.083333334 = -1.313204976
x = -1.313204976

Simplifying
x = -1.313204976


Subproblem 2
x + 4.083333334 = -2.770128358

Simplifying
x + 4.083333334 = -2.770128358

Reorder the terms:
4.083333334 + x = -2.770128358

Solving
4.083333334 + x = -2.770128358

Solving for variable 'x'.

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

Add '-4.083333334' to each side of the equation.
4.083333334 + -4.083333334 + x = -2.770128358 + -4.083333334

Combine like terms: 4.083333334 + -4.083333334 = 0.000000000
0.000000000 + x = -2.770128358 + -4.083333334
x = -2.770128358 + -4.083333334

Combine like terms: -2.770128358 + -4.083333334 = -6.853461692
x = -6.853461692

Simplifying
x = -6.853461692


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.313204976, -6.853461692}
Solution
x = {-1.313204976, -6.853461692}

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