12x^2-264x+989=0

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Solution for 12x^2-264x+989=0 equation: 


Simplifying
12x2 + -264x + 989 = 0

Reorder the terms:
989 + -264x + 12x2 = 0

Solving
989 + -264x + 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'.
82.41666667 + -22x + x2 = 0

Move the constant term to the right:

Add '-82.41666667' to each side of the equation.
82.41666667 + -22x + -82.41666667 + x2 = 0 + -82.41666667

Reorder the terms:
82.41666667 + -82.41666667 + -22x + x2 = 0 + -82.41666667

Combine like terms: 82.41666667 + -82.41666667 = 0.00000000
0.00000000 + -22x + x2 = 0 + -82.41666667
-22x + x2 = 0 + -82.41666667

Combine like terms: 0 + -82.41666667 = -82.41666667
-22x + x2 = -82.41666667

The x term is -22x.  Take half its coefficient (-11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
-22x + 121 + x2 = -82.41666667 + 121

Reorder the terms:
121 + -22x + x2 = -82.41666667 + 121

Combine like terms: -82.41666667 + 121 = 38.58333333
121 + -22x + x2 = 38.58333333

Factor a perfect square on the left side:
(x + -11)(x + -11) = 38.58333333

Calculate the square root of the right side: 6.211548384

Break this problem into two subproblems by setting 
(x + -11) equal to 6.211548384 and -6.211548384.


Subproblem 1
x + -11 = 6.211548384

Simplifying
x + -11 = 6.211548384

Reorder the terms:
-11 + x = 6.211548384

Solving
-11 + x = 6.211548384

Solving for variable 'x'.

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

Add '11' to each side of the equation.
-11 + 11 + x = 6.211548384 + 11

Combine like terms: -11 + 11 = 0
0 + x = 6.211548384 + 11
x = 6.211548384 + 11

Combine like terms: 6.211548384 + 11 = 17.211548384
x = 17.211548384

Simplifying
x = 17.211548384


Subproblem 2
x + -11 = -6.211548384

Simplifying
x + -11 = -6.211548384

Reorder the terms:
-11 + x = -6.211548384

Solving
-11 + x = -6.211548384

Solving for variable 'x'.

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

Add '11' to each side of the equation.
-11 + 11 + x = -6.211548384 + 11

Combine like terms: -11 + 11 = 0
0 + x = -6.211548384 + 11
x = -6.211548384 + 11

Combine like terms: -6.211548384 + 11 = 4.788451616
x = 4.788451616

Simplifying
x = 4.788451616


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.211548384, 4.788451616}

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