6x^2-43x-72=0

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Solution for 6x^2-43x-72=0 equation: 


Simplifying
6x2 + -43x + -72 = 0

Reorder the terms:
-72 + -43x + 6x2 = 0

Solving
-72 + -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'.
-12 + -7.166666667x + x2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -7.166666667x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + -7.166666667x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -7.166666667x + x2 = 0 + 12
-7.166666667x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
-7.166666667x + x2 = 12

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 = 12 + 12.84027778

Reorder the terms:
12.84027778 + -7.166666667x + x2 = 12 + 12.84027778

Combine like terms: 12 + 12.84027778 = 24.84027778
12.84027778 + -7.166666667x + x2 = 24.84027778

Factor a perfect square on the left side:
(x + -3.583333334)(x + -3.583333334) = 24.84027778

Calculate the square root of the right side: 4.984002185

Break this problem into two subproblems by setting 
(x + -3.583333334) equal to 4.984002185 and -4.984002185.


Subproblem 1
x + -3.583333334 = 4.984002185

Simplifying
x + -3.583333334 = 4.984002185

Reorder the terms:
-3.583333334 + x = 4.984002185

Solving
-3.583333334 + x = 4.984002185

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 = 4.984002185 + 3.583333334

Combine like terms: -3.583333334 + 3.583333334 = 0.000000000
0.000000000 + x = 4.984002185 + 3.583333334
x = 4.984002185 + 3.583333334

Combine like terms: 4.984002185 + 3.583333334 = 8.567335519
x = 8.567335519

Simplifying
x = 8.567335519


Subproblem 2
x + -3.583333334 = -4.984002185

Simplifying
x + -3.583333334 = -4.984002185

Reorder the terms:
-3.583333334 + x = -4.984002185

Solving
-3.583333334 + x = -4.984002185

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 = -4.984002185 + 3.583333334

Combine like terms: -3.583333334 + 3.583333334 = 0.000000000
0.000000000 + x = -4.984002185 + 3.583333334
x = -4.984002185 + 3.583333334

Combine like terms: -4.984002185 + 3.583333334 = -1.400668851
x = -1.400668851

Simplifying
x = -1.400668851


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.567335519, -1.400668851}

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