x^2-250x+28=0

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Solution for x^2-250x+28=0 equation: 


Simplifying
x2 + -250x + 28 = 0

Reorder the terms:
28 + -250x + x2 = 0

Solving
28 + -250x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-28' to each side of the equation.
28 + -250x + -28 + x2 = 0 + -28

Reorder the terms:
28 + -28 + -250x + x2 = 0 + -28

Combine like terms: 28 + -28 = 0
0 + -250x + x2 = 0 + -28
-250x + x2 = 0 + -28

Combine like terms: 0 + -28 = -28
-250x + x2 = -28

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 = -28 + 15625

Reorder the terms:
15625 + -250x + x2 = -28 + 15625

Combine like terms: -28 + 15625 = 15597
15625 + -250x + x2 = 15597

Factor a perfect square on the left side:
(x + -125)(x + -125) = 15597

Calculate the square root of the right side: 124.887949779

Break this problem into two subproblems by setting 
(x + -125) equal to 124.887949779 and -124.887949779.


Subproblem 1
x + -125 = 124.887949779

Simplifying
x + -125 = 124.887949779

Reorder the terms:
-125 + x = 124.887949779

Solving
-125 + x = 124.887949779

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 = 124.887949779 + 125

Combine like terms: -125 + 125 = 0
0 + x = 124.887949779 + 125
x = 124.887949779 + 125

Combine like terms: 124.887949779 + 125 = 249.887949779
x = 249.887949779

Simplifying
x = 249.887949779


Subproblem 2
x + -125 = -124.887949779

Simplifying
x + -125 = -124.887949779

Reorder the terms:
-125 + x = -124.887949779

Solving
-125 + x = -124.887949779

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 = -124.887949779 + 125

Combine like terms: -125 + 125 = 0
0 + x = -124.887949779 + 125
x = -124.887949779 + 125

Combine like terms: -124.887949779 + 125 = 0.112050221
x = 0.112050221

Simplifying
x = 0.112050221


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {249.887949779, 0.112050221}

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