15x^2-25x+1=0

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Solution for 15x^2-25x+1=0 equation: 


Simplifying
15x2 + -25x + 1 = 0

Reorder the terms:
1 + -25x + 15x2 = 0

Solving
1 + -25x + 15x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
15 the coefficient of the squared term: 

Divide each side by '15'.
0.06666666667 + -1.666666667x + x2 = 0

Move the constant term to the right:

Add '-0.06666666667' to each side of the equation.
0.06666666667 + -1.666666667x + -0.06666666667 + x2 = 0 + -0.06666666667

Reorder the terms:
0.06666666667 + -0.06666666667 + -1.666666667x + x2 = 0 + -0.06666666667

Combine like terms: 0.06666666667 + -0.06666666667 = 0.00000000000
0.00000000000 + -1.666666667x + x2 = 0 + -0.06666666667
-1.666666667x + x2 = 0 + -0.06666666667

Combine like terms: 0 + -0.06666666667 = -0.06666666667
-1.666666667x + x2 = -0.06666666667

The x term is -1.666666667x.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667x + 0.6944444447 + x2 = -0.06666666667 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667x + x2 = -0.06666666667 + 0.6944444447

Combine like terms: -0.06666666667 + 0.6944444447 = 0.62777777803
0.6944444447 + -1.666666667x + x2 = 0.62777777803

Factor a perfect square on the left side:
(x + -0.8333333335)(x + -0.8333333335) = 0.62777777803

Calculate the square root of the right side: 0.792324288

Break this problem into two subproblems by setting 
(x + -0.8333333335) equal to 0.792324288 and -0.792324288.


Subproblem 1
x + -0.8333333335 = 0.792324288

Simplifying
x + -0.8333333335 = 0.792324288

Reorder the terms:
-0.8333333335 + x = 0.792324288

Solving
-0.8333333335 + x = 0.792324288

Solving for variable 'x'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + x = 0.792324288 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + x = 0.792324288 + 0.8333333335
x = 0.792324288 + 0.8333333335

Combine like terms: 0.792324288 + 0.8333333335 = 1.6256576215
x = 1.6256576215

Simplifying
x = 1.6256576215


Subproblem 2
x + -0.8333333335 = -0.792324288

Simplifying
x + -0.8333333335 = -0.792324288

Reorder the terms:
-0.8333333335 + x = -0.792324288

Solving
-0.8333333335 + x = -0.792324288

Solving for variable 'x'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + x = -0.792324288 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + x = -0.792324288 + 0.8333333335
x = -0.792324288 + 0.8333333335

Combine like terms: -0.792324288 + 0.8333333335 = 0.0410090455
x = 0.0410090455

Simplifying
x = 0.0410090455


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.6256576215, 0.0410090455}

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