6x^2-70x+125=0

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Solution for 6x^2-70x+125=0 equation: 


Simplifying
6x2 + -70x + 125 = 0

Reorder the terms:
125 + -70x + 6x2 = 0

Solving
125 + -70x + 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'.
20.83333333 + -11.66666667x + x2 = 0

Move the constant term to the right:

Add '-20.83333333' to each side of the equation.
20.83333333 + -11.66666667x + -20.83333333 + x2 = 0 + -20.83333333

Reorder the terms:
20.83333333 + -20.83333333 + -11.66666667x + x2 = 0 + -20.83333333

Combine like terms: 20.83333333 + -20.83333333 = 0.00000000
0.00000000 + -11.66666667x + x2 = 0 + -20.83333333
-11.66666667x + x2 = 0 + -20.83333333

Combine like terms: 0 + -20.83333333 = -20.83333333
-11.66666667x + x2 = -20.83333333

The x term is -11.66666667x.  Take half its coefficient (-5.833333335).
Square it (34.02777780) and add it to both sides.

Add '34.02777780' to each side of the equation.
-11.66666667x + 34.02777780 + x2 = -20.83333333 + 34.02777780

Reorder the terms:
34.02777780 + -11.66666667x + x2 = -20.83333333 + 34.02777780

Combine like terms: -20.83333333 + 34.02777780 = 13.19444447
34.02777780 + -11.66666667x + x2 = 13.19444447

Factor a perfect square on the left side:
(x + -5.833333335)(x + -5.833333335) = 13.19444447

Calculate the square root of the right side: 3.63241579

Break this problem into two subproblems by setting 
(x + -5.833333335) equal to 3.63241579 and -3.63241579.


Subproblem 1
x + -5.833333335 = 3.63241579

Simplifying
x + -5.833333335 = 3.63241579

Reorder the terms:
-5.833333335 + x = 3.63241579

Solving
-5.833333335 + x = 3.63241579

Solving for variable 'x'.

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

Add '5.833333335' to each side of the equation.
-5.833333335 + 5.833333335 + x = 3.63241579 + 5.833333335

Combine like terms: -5.833333335 + 5.833333335 = 0.000000000
0.000000000 + x = 3.63241579 + 5.833333335
x = 3.63241579 + 5.833333335

Combine like terms: 3.63241579 + 5.833333335 = 9.465749125
x = 9.465749125

Simplifying
x = 9.465749125


Subproblem 2
x + -5.833333335 = -3.63241579

Simplifying
x + -5.833333335 = -3.63241579

Reorder the terms:
-5.833333335 + x = -3.63241579

Solving
-5.833333335 + x = -3.63241579

Solving for variable 'x'.

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

Add '5.833333335' to each side of the equation.
-5.833333335 + 5.833333335 + x = -3.63241579 + 5.833333335

Combine like terms: -5.833333335 + 5.833333335 = 0.000000000
0.000000000 + x = -3.63241579 + 5.833333335
x = -3.63241579 + 5.833333335

Combine like terms: -3.63241579 + 5.833333335 = 2.200917545
x = 2.200917545

Simplifying
x = 2.200917545


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.465749125, 2.200917545}

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