6x^2-47x+82=0

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Solution for 6x^2-47x+82=0 equation: 


Simplifying
6x2 + -47x + 82 = 0

Reorder the terms:
82 + -47x + 6x2 = 0

Solving
82 + -47x + 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'.
13.66666667 + -7.833333333x + x2 = 0

Move the constant term to the right:

Add '-13.66666667' to each side of the equation.
13.66666667 + -7.833333333x + -13.66666667 + x2 = 0 + -13.66666667

Reorder the terms:
13.66666667 + -13.66666667 + -7.833333333x + x2 = 0 + -13.66666667

Combine like terms: 13.66666667 + -13.66666667 = 0.00000000
0.00000000 + -7.833333333x + x2 = 0 + -13.66666667
-7.833333333x + x2 = 0 + -13.66666667

Combine like terms: 0 + -13.66666667 = -13.66666667
-7.833333333x + x2 = -13.66666667

The x term is -7.833333333x.  Take half its coefficient (-3.916666667).
Square it (15.34027778) and add it to both sides.

Add '15.34027778' to each side of the equation.
-7.833333333x + 15.34027778 + x2 = -13.66666667 + 15.34027778

Reorder the terms:
15.34027778 + -7.833333333x + x2 = -13.66666667 + 15.34027778

Combine like terms: -13.66666667 + 15.34027778 = 1.67361111
15.34027778 + -7.833333333x + x2 = 1.67361111

Factor a perfect square on the left side:
(x + -3.916666667)(x + -3.916666667) = 1.67361111

Calculate the square root of the right side: 1.293681224

Break this problem into two subproblems by setting 
(x + -3.916666667) equal to 1.293681224 and -1.293681224.


Subproblem 1
x + -3.916666667 = 1.293681224

Simplifying
x + -3.916666667 = 1.293681224

Reorder the terms:
-3.916666667 + x = 1.293681224

Solving
-3.916666667 + x = 1.293681224

Solving for variable 'x'.

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

Add '3.916666667' to each side of the equation.
-3.916666667 + 3.916666667 + x = 1.293681224 + 3.916666667

Combine like terms: -3.916666667 + 3.916666667 = 0.000000000
0.000000000 + x = 1.293681224 + 3.916666667
x = 1.293681224 + 3.916666667

Combine like terms: 1.293681224 + 3.916666667 = 5.210347891
x = 5.210347891

Simplifying
x = 5.210347891


Subproblem 2
x + -3.916666667 = -1.293681224

Simplifying
x + -3.916666667 = -1.293681224

Reorder the terms:
-3.916666667 + x = -1.293681224

Solving
-3.916666667 + x = -1.293681224

Solving for variable 'x'.

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

Add '3.916666667' to each side of the equation.
-3.916666667 + 3.916666667 + x = -1.293681224 + 3.916666667

Combine like terms: -3.916666667 + 3.916666667 = 0.000000000
0.000000000 + x = -1.293681224 + 3.916666667
x = -1.293681224 + 3.916666667

Combine like terms: -1.293681224 + 3.916666667 = 2.622985443
x = 2.622985443

Simplifying
x = 2.622985443


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.210347891, 2.622985443}

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