x=12x^2-88x+121

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Solution for x=12x^2-88x+121 equation:


Simplifying
x = 12x2 + -88x + 121

Reorder the terms:
x = 121 + -88x + 12x2

Solving
x = 121 + -88x + 12x2

Solving for variable 'x'.

Reorder the terms:
-121 + x + 88x + -12x2 = 121 + -88x + 12x2 + -121 + 88x + -12x2

Combine like terms: x + 88x = 89x
-121 + 89x + -12x2 = 121 + -88x + 12x2 + -121 + 88x + -12x2

Reorder the terms:
-121 + 89x + -12x2 = 121 + -121 + -88x + 88x + 12x2 + -12x2

Combine like terms: 121 + -121 = 0
-121 + 89x + -12x2 = 0 + -88x + 88x + 12x2 + -12x2
-121 + 89x + -12x2 = -88x + 88x + 12x2 + -12x2

Combine like terms: -88x + 88x = 0
-121 + 89x + -12x2 = 0 + 12x2 + -12x2
-121 + 89x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
-121 + 89x + -12x2 = 0

Begin completing the square.  Divide all terms by
-12 the coefficient of the squared term: 

Divide each side by '-12'.
10.08333333 + -7.416666667x + x2 = 0

Move the constant term to the right:

Add '-10.08333333' to each side of the equation.
10.08333333 + -7.416666667x + -10.08333333 + x2 = 0 + -10.08333333

Reorder the terms:
10.08333333 + -10.08333333 + -7.416666667x + x2 = 0 + -10.08333333

Combine like terms: 10.08333333 + -10.08333333 = 0.00000000
0.00000000 + -7.416666667x + x2 = 0 + -10.08333333
-7.416666667x + x2 = 0 + -10.08333333

Combine like terms: 0 + -10.08333333 = -10.08333333
-7.416666667x + x2 = -10.08333333

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 = -10.08333333 + 13.75173612

Reorder the terms:
13.75173612 + -7.416666667x + x2 = -10.08333333 + 13.75173612

Combine like terms: -10.08333333 + 13.75173612 = 3.66840279
13.75173612 + -7.416666667x + x2 = 3.66840279

Factor a perfect square on the left side:
(x + -3.708333334)(x + -3.708333334) = 3.66840279

Calculate the square root of the right side: 1.915307492

Break this problem into two subproblems by setting 
(x + -3.708333334) equal to 1.915307492 and -1.915307492.

Subproblem 1

x + -3.708333334 = 1.915307492 Simplifying x + -3.708333334 = 1.915307492 Reorder the terms: -3.708333334 + x = 1.915307492 Solving -3.708333334 + x = 1.915307492 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 = 1.915307492 + 3.708333334 Combine like terms: -3.708333334 + 3.708333334 = 0.000000000 0.000000000 + x = 1.915307492 + 3.708333334 x = 1.915307492 + 3.708333334 Combine like terms: 1.915307492 + 3.708333334 = 5.623640826 x = 5.623640826 Simplifying x = 5.623640826

Subproblem 2

x + -3.708333334 = -1.915307492 Simplifying x + -3.708333334 = -1.915307492 Reorder the terms: -3.708333334 + x = -1.915307492 Solving -3.708333334 + x = -1.915307492 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 = -1.915307492 + 3.708333334 Combine like terms: -3.708333334 + 3.708333334 = 0.000000000 0.000000000 + x = -1.915307492 + 3.708333334 x = -1.915307492 + 3.708333334 Combine like terms: -1.915307492 + 3.708333334 = 1.793025842 x = 1.793025842 Simplifying x = 1.793025842

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.623640826, 1.793025842}

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