12x^2-51x-140=0

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Solution for 12x^2-51x-140=0 equation: 


Simplifying
12x2 + -51x + -140 = 0

Reorder the terms:
-140 + -51x + 12x2 = 0

Solving
-140 + -51x + 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'.
-11.66666667 + -4.25x + x2 = 0

Move the constant term to the right:

Add '11.66666667' to each side of the equation.
-11.66666667 + -4.25x + 11.66666667 + x2 = 0 + 11.66666667

Reorder the terms:
-11.66666667 + 11.66666667 + -4.25x + x2 = 0 + 11.66666667

Combine like terms: -11.66666667 + 11.66666667 = 0.00000000
0.00000000 + -4.25x + x2 = 0 + 11.66666667
-4.25x + x2 = 0 + 11.66666667

Combine like terms: 0 + 11.66666667 = 11.66666667
-4.25x + x2 = 11.66666667

The x term is -4.25x.  Take half its coefficient (-2.125).
Square it (4.515625) and add it to both sides.

Add '4.515625' to each side of the equation.
-4.25x + 4.515625 + x2 = 11.66666667 + 4.515625

Reorder the terms:
4.515625 + -4.25x + x2 = 11.66666667 + 4.515625

Combine like terms: 11.66666667 + 4.515625 = 16.18229167
4.515625 + -4.25x + x2 = 16.18229167

Factor a perfect square on the left side:
(x + -2.125)(x + -2.125) = 16.18229167

Calculate the square root of the right side: 4.022721923

Break this problem into two subproblems by setting 
(x + -2.125) equal to 4.022721923 and -4.022721923.


Subproblem 1
x + -2.125 = 4.022721923

Simplifying
x + -2.125 = 4.022721923

Reorder the terms:
-2.125 + x = 4.022721923

Solving
-2.125 + x = 4.022721923

Solving for variable 'x'.

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

Add '2.125' to each side of the equation.
-2.125 + 2.125 + x = 4.022721923 + 2.125

Combine like terms: -2.125 + 2.125 = 0.000
0.000 + x = 4.022721923 + 2.125
x = 4.022721923 + 2.125

Combine like terms: 4.022721923 + 2.125 = 6.147721923
x = 6.147721923

Simplifying
x = 6.147721923


Subproblem 2
x + -2.125 = -4.022721923

Simplifying
x + -2.125 = -4.022721923

Reorder the terms:
-2.125 + x = -4.022721923

Solving
-2.125 + x = -4.022721923

Solving for variable 'x'.

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

Add '2.125' to each side of the equation.
-2.125 + 2.125 + x = -4.022721923 + 2.125

Combine like terms: -2.125 + 2.125 = 0.000
0.000 + x = -4.022721923 + 2.125
x = -4.022721923 + 2.125

Combine like terms: -4.022721923 + 2.125 = -1.897721923
x = -1.897721923

Simplifying
x = -1.897721923


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.147721923, -1.897721923}

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