12x^2+89x+163=0

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Solution for 12x^2+89x+163=0 equation: 


Simplifying
12x2 + 89x + 163 = 0

Reorder the terms:
163 + 89x + 12x2 = 0

Solving
163 + 89x + 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'.
13.58333333 + 7.416666667x + x2 = 0

Move the constant term to the right:

Add '-13.58333333' to each side of the equation.
13.58333333 + 7.416666667x + -13.58333333 + x2 = 0 + -13.58333333

Reorder the terms:
13.58333333 + -13.58333333 + 7.416666667x + x2 = 0 + -13.58333333

Combine like terms: 13.58333333 + -13.58333333 = 0.00000000
0.00000000 + 7.416666667x + x2 = 0 + -13.58333333
7.416666667x + x2 = 0 + -13.58333333

Combine like terms: 0 + -13.58333333 = -13.58333333
7.416666667x + x2 = -13.58333333

The x term is 7.416666667x.  Take half its coefficient (3.708333334).
Square it (13.75173612) and add it to both sides.

Add '13.75173612' to each side of the equation.
7.416666667x + 13.75173612 + x2 = -13.58333333 + 13.75173612

Reorder the terms:
13.75173612 + 7.416666667x + x2 = -13.58333333 + 13.75173612

Combine like terms: -13.58333333 + 13.75173612 = 0.16840279
13.75173612 + 7.416666667x + x2 = 0.16840279

Factor a perfect square on the left side:
(x + 3.708333334)(x + 3.708333334) = 0.16840279

Calculate the square root of the right side: 0.41036909

Break this problem into two subproblems by setting 
(x + 3.708333334) equal to 0.41036909 and -0.41036909.


Subproblem 1
x + 3.708333334 = 0.41036909

Simplifying
x + 3.708333334 = 0.41036909

Reorder the terms:
3.708333334 + x = 0.41036909

Solving
3.708333334 + x = 0.41036909

Solving for variable 'x'.

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

Add '-3.708333334' to each side of the equation.
3.708333334 + -3.708333334 + x = 0.41036909 + -3.708333334

Combine like terms: 3.708333334 + -3.708333334 = 0.000000000
0.000000000 + x = 0.41036909 + -3.708333334
x = 0.41036909 + -3.708333334

Combine like terms: 0.41036909 + -3.708333334 = -3.297964244
x = -3.297964244

Simplifying
x = -3.297964244


Subproblem 2
x + 3.708333334 = -0.41036909

Simplifying
x + 3.708333334 = -0.41036909

Reorder the terms:
3.708333334 + x = -0.41036909

Solving
3.708333334 + x = -0.41036909

Solving for variable 'x'.

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

Add '-3.708333334' to each side of the equation.
3.708333334 + -3.708333334 + x = -0.41036909 + -3.708333334

Combine like terms: 3.708333334 + -3.708333334 = 0.000000000
0.000000000 + x = -0.41036909 + -3.708333334
x = -0.41036909 + -3.708333334

Combine like terms: -0.41036909 + -3.708333334 = -4.118702424
x = -4.118702424

Simplifying
x = -4.118702424


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.297964244, -4.118702424}

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