6x^2-40x+25=0

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Solution for 6x^2-40x+25=0 equation: 


Simplifying
6x2 + -40x + 25 = 0

Reorder the terms:
25 + -40x + 6x2 = 0

Solving
25 + -40x + 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 + -6.666666667x + x2 = 0

Move the constant term to the right:

Add '-4.166666667' to each side of the equation.
4.166666667 + -6.666666667x + -4.166666667 + x2 = 0 + -4.166666667

Reorder the terms:
4.166666667 + -4.166666667 + -6.666666667x + x2 = 0 + -4.166666667

Combine like terms: 4.166666667 + -4.166666667 = 0.000000000
0.000000000 + -6.666666667x + x2 = 0 + -4.166666667
-6.666666667x + x2 = 0 + -4.166666667

Combine like terms: 0 + -4.166666667 = -4.166666667
-6.666666667x + x2 = -4.166666667

The x term is -6.666666667x.  Take half its coefficient (-3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
-6.666666667x + 11.11111112 + x2 = -4.166666667 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667x + x2 = -4.166666667 + 11.11111112

Combine like terms: -4.166666667 + 11.11111112 = 6.944444453
11.11111112 + -6.666666667x + x2 = 6.944444453

Factor a perfect square on the left side:
(x + -3.333333334)(x + -3.333333334) = 6.944444453

Calculate the square root of the right side: 2.635231385

Break this problem into two subproblems by setting 
(x + -3.333333334) equal to 2.635231385 and -2.635231385.


Subproblem 1
x + -3.333333334 = 2.635231385

Simplifying
x + -3.333333334 = 2.635231385

Reorder the terms:
-3.333333334 + x = 2.635231385

Solving
-3.333333334 + x = 2.635231385

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = 2.635231385 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = 2.635231385 + 3.333333334
x = 2.635231385 + 3.333333334

Combine like terms: 2.635231385 + 3.333333334 = 5.968564719
x = 5.968564719

Simplifying
x = 5.968564719


Subproblem 2
x + -3.333333334 = -2.635231385

Simplifying
x + -3.333333334 = -2.635231385

Reorder the terms:
-3.333333334 + x = -2.635231385

Solving
-3.333333334 + x = -2.635231385

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = -2.635231385 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = -2.635231385 + 3.333333334
x = -2.635231385 + 3.333333334

Combine like terms: -2.635231385 + 3.333333334 = 0.698101949
x = 0.698101949

Simplifying
x = 0.698101949


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.968564719, 0.698101949}

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