x^2-250x+15625=20625

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Solution for x^2-250x+15625=20625 equation: 


Simplifying
x2 + -250x + 15625 = 20625

Reorder the terms:
15625 + -250x + x2 = 20625

Solving
15625 + -250x + x2 = 20625

Solving for variable 'x'.

Reorder the terms:
15625 + -20625 + -250x + x2 = 20625 + -20625

Combine like terms: 15625 + -20625 = -5000
-5000 + -250x + x2 = 20625 + -20625

Combine like terms: 20625 + -20625 = 0
-5000 + -250x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5000' to each side of the equation.
-5000 + -250x + 5000 + x2 = 0 + 5000

Reorder the terms:
-5000 + 5000 + -250x + x2 = 0 + 5000

Combine like terms: -5000 + 5000 = 0
0 + -250x + x2 = 0 + 5000
-250x + x2 = 0 + 5000

Combine like terms: 0 + 5000 = 5000
-250x + x2 = 5000

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 = 5000 + 15625

Reorder the terms:
15625 + -250x + x2 = 5000 + 15625

Combine like terms: 5000 + 15625 = 20625
15625 + -250x + x2 = 20625

Factor a perfect square on the left side:
(x + -125)(x + -125) = 20625

Calculate the square root of the right side: 143.614066163

Break this problem into two subproblems by setting 
(x + -125) equal to 143.614066163 and -143.614066163.


Subproblem 1
x + -125 = 143.614066163

Simplifying
x + -125 = 143.614066163

Reorder the terms:
-125 + x = 143.614066163

Solving
-125 + x = 143.614066163

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 = 143.614066163 + 125

Combine like terms: -125 + 125 = 0
0 + x = 143.614066163 + 125
x = 143.614066163 + 125

Combine like terms: 143.614066163 + 125 = 268.614066163
x = 268.614066163

Simplifying
x = 268.614066163


Subproblem 2
x + -125 = -143.614066163

Simplifying
x + -125 = -143.614066163

Reorder the terms:
-125 + x = -143.614066163

Solving
-125 + x = -143.614066163

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 = -143.614066163 + 125

Combine like terms: -125 + 125 = 0
0 + x = -143.614066163 + 125
x = -143.614066163 + 125

Combine like terms: -143.614066163 + 125 = -18.614066163
x = -18.614066163

Simplifying
x = -18.614066163


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {268.614066163, -18.614066163}

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