6x^2-43x-112=0

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Solution for 6x^2-43x-112=0 equation: 


Simplifying
6x2 + -43x + -112 = 0

Reorder the terms:
-112 + -43x + 6x2 = 0

Solving
-112 + -43x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
-18.66666667 + -7.166666667x + x2 = 0

Move the constant term to the right:

Add '18.66666667' to each side of the equation.
-18.66666667 + -7.166666667x + 18.66666667 + x2 = 0 + 18.66666667

Reorder the terms:
-18.66666667 + 18.66666667 + -7.166666667x + x2 = 0 + 18.66666667

Combine like terms: -18.66666667 + 18.66666667 = 0.00000000
0.00000000 + -7.166666667x + x2 = 0 + 18.66666667
-7.166666667x + x2 = 0 + 18.66666667

Combine like terms: 0 + 18.66666667 = 18.66666667
-7.166666667x + x2 = 18.66666667

The x term is -7.166666667x.  Take half its coefficient (-3.583333334).
Square it (12.84027778) and add it to both sides.

Add '12.84027778' to each side of the equation.
-7.166666667x + 12.84027778 + x2 = 18.66666667 + 12.84027778

Reorder the terms:
12.84027778 + -7.166666667x + x2 = 18.66666667 + 12.84027778

Combine like terms: 18.66666667 + 12.84027778 = 31.50694445
12.84027778 + -7.166666667x + x2 = 31.50694445

Factor a perfect square on the left side:
(x + -3.583333334)(x + -3.583333334) = 31.50694445

Calculate the square root of the right side: 5.613104707

Break this problem into two subproblems by setting 
(x + -3.583333334) equal to 5.613104707 and -5.613104707.


Subproblem 1
x + -3.583333334 = 5.613104707

Simplifying
x + -3.583333334 = 5.613104707

Reorder the terms:
-3.583333334 + x = 5.613104707

Solving
-3.583333334 + x = 5.613104707

Solving for variable 'x'.

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

Add '3.583333334' to each side of the equation.
-3.583333334 + 3.583333334 + x = 5.613104707 + 3.583333334

Combine like terms: -3.583333334 + 3.583333334 = 0.000000000
0.000000000 + x = 5.613104707 + 3.583333334
x = 5.613104707 + 3.583333334

Combine like terms: 5.613104707 + 3.583333334 = 9.196438041
x = 9.196438041

Simplifying
x = 9.196438041


Subproblem 2
x + -3.583333334 = -5.613104707

Simplifying
x + -3.583333334 = -5.613104707

Reorder the terms:
-3.583333334 + x = -5.613104707

Solving
-3.583333334 + x = -5.613104707

Solving for variable 'x'.

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

Add '3.583333334' to each side of the equation.
-3.583333334 + 3.583333334 + x = -5.613104707 + 3.583333334

Combine like terms: -3.583333334 + 3.583333334 = 0.000000000
0.000000000 + x = -5.613104707 + 3.583333334
x = -5.613104707 + 3.583333334

Combine like terms: -5.613104707 + 3.583333334 = -2.029771373
x = -2.029771373

Simplifying
x = -2.029771373


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.196438041, -2.029771373}

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