6x^2-41x+56=0

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Solution for 6x^2-41x+56=0 equation: 


Simplifying
6x2 + -41x + 56 = 0

Reorder the terms:
56 + -41x + 6x2 = 0

Solving
56 + -41x + 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'.
9.333333333 + -6.833333333x + x2 = 0

Move the constant term to the right:

Add '-9.333333333' to each side of the equation.
9.333333333 + -6.833333333x + -9.333333333 + x2 = 0 + -9.333333333

Reorder the terms:
9.333333333 + -9.333333333 + -6.833333333x + x2 = 0 + -9.333333333

Combine like terms: 9.333333333 + -9.333333333 = 0.000000000
0.000000000 + -6.833333333x + x2 = 0 + -9.333333333
-6.833333333x + x2 = 0 + -9.333333333

Combine like terms: 0 + -9.333333333 = -9.333333333
-6.833333333x + x2 = -9.333333333

The x term is -6.833333333x.  Take half its coefficient (-3.416666667).
Square it (11.67361111) and add it to both sides.

Add '11.67361111' to each side of the equation.
-6.833333333x + 11.67361111 + x2 = -9.333333333 + 11.67361111

Reorder the terms:
11.67361111 + -6.833333333x + x2 = -9.333333333 + 11.67361111

Combine like terms: -9.333333333 + 11.67361111 = 2.340277777
11.67361111 + -6.833333333x + x2 = 2.340277777

Factor a perfect square on the left side:
(x + -3.416666667)(x + -3.416666667) = 2.340277777

Calculate the square root of the right side: 1.529796646

Break this problem into two subproblems by setting 
(x + -3.416666667) equal to 1.529796646 and -1.529796646.


Subproblem 1
x + -3.416666667 = 1.529796646

Simplifying
x + -3.416666667 = 1.529796646

Reorder the terms:
-3.416666667 + x = 1.529796646

Solving
-3.416666667 + x = 1.529796646

Solving for variable 'x'.

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

Add '3.416666667' to each side of the equation.
-3.416666667 + 3.416666667 + x = 1.529796646 + 3.416666667

Combine like terms: -3.416666667 + 3.416666667 = 0.000000000
0.000000000 + x = 1.529796646 + 3.416666667
x = 1.529796646 + 3.416666667

Combine like terms: 1.529796646 + 3.416666667 = 4.946463313
x = 4.946463313

Simplifying
x = 4.946463313


Subproblem 2
x + -3.416666667 = -1.529796646

Simplifying
x + -3.416666667 = -1.529796646

Reorder the terms:
-3.416666667 + x = -1.529796646

Solving
-3.416666667 + x = -1.529796646

Solving for variable 'x'.

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

Add '3.416666667' to each side of the equation.
-3.416666667 + 3.416666667 + x = -1.529796646 + 3.416666667

Combine like terms: -3.416666667 + 3.416666667 = 0.000000000
0.000000000 + x = -1.529796646 + 3.416666667
x = -1.529796646 + 3.416666667

Combine like terms: -1.529796646 + 3.416666667 = 1.886870021
x = 1.886870021

Simplifying
x = 1.886870021


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.946463313, 1.886870021}

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