6x^2-50x+25=0

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Solution for 6x^2-50x+25=0 equation: 


Simplifying
6x2 + -50x + 25 = 0

Reorder the terms:
25 + -50x + 6x2 = 0

Solving
25 + -50x + 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'.
4.166666667 + -8.333333333x + x2 = 0

Move the constant term to the right:

Add '-4.166666667' to each side of the equation.
4.166666667 + -8.333333333x + -4.166666667 + x2 = 0 + -4.166666667

Reorder the terms:
4.166666667 + -4.166666667 + -8.333333333x + x2 = 0 + -4.166666667

Combine like terms: 4.166666667 + -4.166666667 = 0.000000000
0.000000000 + -8.333333333x + x2 = 0 + -4.166666667
-8.333333333x + x2 = 0 + -4.166666667

Combine like terms: 0 + -4.166666667 = -4.166666667
-8.333333333x + x2 = -4.166666667

The x term is -8.333333333x.  Take half its coefficient (-4.166666667).
Square it (17.36111111) and add it to both sides.

Add '17.36111111' to each side of the equation.
-8.333333333x + 17.36111111 + x2 = -4.166666667 + 17.36111111

Reorder the terms:
17.36111111 + -8.333333333x + x2 = -4.166666667 + 17.36111111

Combine like terms: -4.166666667 + 17.36111111 = 13.194444443
17.36111111 + -8.333333333x + x2 = 13.194444443

Factor a perfect square on the left side:
(x + -4.166666667)(x + -4.166666667) = 13.194444443

Calculate the square root of the right side: 3.632415786

Break this problem into two subproblems by setting 
(x + -4.166666667) equal to 3.632415786 and -3.632415786.


Subproblem 1
x + -4.166666667 = 3.632415786

Simplifying
x + -4.166666667 = 3.632415786

Reorder the terms:
-4.166666667 + x = 3.632415786

Solving
-4.166666667 + x = 3.632415786

Solving for variable 'x'.

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

Add '4.166666667' to each side of the equation.
-4.166666667 + 4.166666667 + x = 3.632415786 + 4.166666667

Combine like terms: -4.166666667 + 4.166666667 = 0.000000000
0.000000000 + x = 3.632415786 + 4.166666667
x = 3.632415786 + 4.166666667

Combine like terms: 3.632415786 + 4.166666667 = 7.799082453
x = 7.799082453

Simplifying
x = 7.799082453


Subproblem 2
x + -4.166666667 = -3.632415786

Simplifying
x + -4.166666667 = -3.632415786

Reorder the terms:
-4.166666667 + x = -3.632415786

Solving
-4.166666667 + x = -3.632415786

Solving for variable 'x'.

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

Add '4.166666667' to each side of the equation.
-4.166666667 + 4.166666667 + x = -3.632415786 + 4.166666667

Combine like terms: -4.166666667 + 4.166666667 = 0.000000000
0.000000000 + x = -3.632415786 + 4.166666667
x = -3.632415786 + 4.166666667

Combine like terms: -3.632415786 + 4.166666667 = 0.534250881
x = 0.534250881

Simplifying
x = 0.534250881


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.799082453, 0.534250881}

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