x^2-250x+125=0

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Solution for x^2-250x+125=0 equation: 


Simplifying
x2 + -250x + 125 = 0

Reorder the terms:
125 + -250x + x2 = 0

Solving
125 + -250x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-125' to each side of the equation.
125 + -250x + -125 + x2 = 0 + -125

Reorder the terms:
125 + -125 + -250x + x2 = 0 + -125

Combine like terms: 125 + -125 = 0
0 + -250x + x2 = 0 + -125
-250x + x2 = 0 + -125

Combine like terms: 0 + -125 = -125
-250x + x2 = -125

The x term is -250x.  Take half its coefficient (-125).
Square it (15625) and add it to both sides.

Add '15625' to each side of the equation.
-250x + 15625 + x2 = -125 + 15625

Reorder the terms:
15625 + -250x + x2 = -125 + 15625

Combine like terms: -125 + 15625 = 15500
15625 + -250x + x2 = 15500

Factor a perfect square on the left side:
(x + -125)(x + -125) = 15500

Calculate the square root of the right side: 124.49899598

Break this problem into two subproblems by setting 
(x + -125) equal to 124.49899598 and -124.49899598.


Subproblem 1
x + -125 = 124.49899598

Simplifying
x + -125 = 124.49899598

Reorder the terms:
-125 + x = 124.49899598

Solving
-125 + x = 124.49899598

Solving for variable 'x'.

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

Add '125' to each side of the equation.
-125 + 125 + x = 124.49899598 + 125

Combine like terms: -125 + 125 = 0
0 + x = 124.49899598 + 125
x = 124.49899598 + 125

Combine like terms: 124.49899598 + 125 = 249.49899598
x = 249.49899598

Simplifying
x = 249.49899598


Subproblem 2
x + -125 = -124.49899598

Simplifying
x + -125 = -124.49899598

Reorder the terms:
-125 + x = -124.49899598

Solving
-125 + x = -124.49899598

Solving for variable 'x'.

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

Add '125' to each side of the equation.
-125 + 125 + x = -124.49899598 + 125

Combine like terms: -125 + 125 = 0
0 + x = -124.49899598 + 125
x = -124.49899598 + 125

Combine like terms: -124.49899598 + 125 = 0.50100402
x = 0.50100402

Simplifying
x = 0.50100402


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {249.49899598, 0.50100402}

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