12x^2-123x+118=0

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Solution for 12x^2-123x+118=0 equation:


Simplifying
12x2 + -123x + 118 = 0

Reorder the terms:
118 + -123x + 12x2 = 0

Solving
118 + -123x + 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'.
9.833333333 + -10.25x + x2 = 0

Move the constant term to the right:

Add '-9.833333333' to each side of the equation.
9.833333333 + -10.25x + -9.833333333 + x2 = 0 + -9.833333333

Reorder the terms:
9.833333333 + -9.833333333 + -10.25x + x2 = 0 + -9.833333333

Combine like terms: 9.833333333 + -9.833333333 = 0.000000000
0.000000000 + -10.25x + x2 = 0 + -9.833333333
-10.25x + x2 = 0 + -9.833333333

Combine like terms: 0 + -9.833333333 = -9.833333333
-10.25x + x2 = -9.833333333

The x term is -10.25x.  Take half its coefficient (-5.125).
Square it (26.265625) and add it to both sides.

Add '26.265625' to each side of the equation.
-10.25x + 26.265625 + x2 = -9.833333333 + 26.265625

Reorder the terms:
26.265625 + -10.25x + x2 = -9.833333333 + 26.265625

Combine like terms: -9.833333333 + 26.265625 = 16.432291667
26.265625 + -10.25x + x2 = 16.432291667

Factor a perfect square on the left side:
(x + -5.125)(x + -5.125) = 16.432291667

Calculate the square root of the right side: 4.053676315

Break this problem into two subproblems by setting 
(x + -5.125) equal to 4.053676315 and -4.053676315.

Subproblem 1

x + -5.125 = 4.053676315 Simplifying x + -5.125 = 4.053676315 Reorder the terms: -5.125 + x = 4.053676315 Solving -5.125 + x = 4.053676315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.125' to each side of the equation. -5.125 + 5.125 + x = 4.053676315 + 5.125 Combine like terms: -5.125 + 5.125 = 0.000 0.000 + x = 4.053676315 + 5.125 x = 4.053676315 + 5.125 Combine like terms: 4.053676315 + 5.125 = 9.178676315 x = 9.178676315 Simplifying x = 9.178676315

Subproblem 2

x + -5.125 = -4.053676315 Simplifying x + -5.125 = -4.053676315 Reorder the terms: -5.125 + x = -4.053676315 Solving -5.125 + x = -4.053676315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.125' to each side of the equation. -5.125 + 5.125 + x = -4.053676315 + 5.125 Combine like terms: -5.125 + 5.125 = 0.000 0.000 + x = -4.053676315 + 5.125 x = -4.053676315 + 5.125 Combine like terms: -4.053676315 + 5.125 = 1.071323685 x = 1.071323685 Simplifying x = 1.071323685

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.178676315, 1.071323685}

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