0.375x^2-125x-1=0

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Solution for 0.375x^2-125x-1=0 equation: 


Simplifying
0.375x2 + -125x + -1 = 0

Reorder the terms:
-1 + -125x + 0.375x2 = 0

Solving
-1 + -125x + 0.375x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.375'.
-2.666666667 + -333.3333333x + x2 = 0

Move the constant term to the right:

Add '2.666666667' to each side of the equation.
-2.666666667 + -333.3333333x + 2.666666667 + x2 = 0 + 2.666666667

Reorder the terms:
-2.666666667 + 2.666666667 + -333.3333333x + x2 = 0 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + -333.3333333x + x2 = 0 + 2.666666667
-333.3333333x + x2 = 0 + 2.666666667

Combine like terms: 0 + 2.666666667 = 2.666666667
-333.3333333x + x2 = 2.666666667

The x term is -333.3333333x.  Take half its coefficient (-166.6666667).
Square it (27777.77779) and add it to both sides.

Add '27777.77779' to each side of the equation.
-333.3333333x + 27777.77779 + x2 = 2.666666667 + 27777.77779

Reorder the terms:
27777.77779 + -333.3333333x + x2 = 2.666666667 + 27777.77779

Combine like terms: 2.666666667 + 27777.77779 = 27780.444456667
27777.77779 + -333.3333333x + x2 = 27780.444456667

Factor a perfect square on the left side:
(x + -166.6666667)(x + -166.6666667) = 27780.444456667

Calculate the square root of the right side: 166.674666511

Break this problem into two subproblems by setting 
(x + -166.6666667) equal to 166.674666511 and -166.674666511.


Subproblem 1
x + -166.6666667 = 166.674666511

Simplifying
x + -166.6666667 = 166.674666511

Reorder the terms:
-166.6666667 + x = 166.674666511

Solving
-166.6666667 + x = 166.674666511

Solving for variable 'x'.

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

Add '166.6666667' to each side of the equation.
-166.6666667 + 166.6666667 + x = 166.674666511 + 166.6666667

Combine like terms: -166.6666667 + 166.6666667 = 0.0000000
0.0000000 + x = 166.674666511 + 166.6666667
x = 166.674666511 + 166.6666667

Combine like terms: 166.674666511 + 166.6666667 = 333.341333211
x = 333.341333211

Simplifying
x = 333.341333211


Subproblem 2
x + -166.6666667 = -166.674666511

Simplifying
x + -166.6666667 = -166.674666511

Reorder the terms:
-166.6666667 + x = -166.674666511

Solving
-166.6666667 + x = -166.674666511

Solving for variable 'x'.

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

Add '166.6666667' to each side of the equation.
-166.6666667 + 166.6666667 + x = -166.674666511 + 166.6666667

Combine like terms: -166.6666667 + 166.6666667 = 0.0000000
0.0000000 + x = -166.674666511 + 166.6666667
x = -166.674666511 + 166.6666667

Combine like terms: -166.674666511 + 166.6666667 = -0.007999811
x = -0.007999811

Simplifying
x = -0.007999811


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {333.341333211, -0.007999811}

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