x^2-2025x+50625=0

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Solution for x^2-2025x+50625=0 equation: 


Simplifying
x2 + -2025x + 50625 = 0

Reorder the terms:
50625 + -2025x + x2 = 0

Solving
50625 + -2025x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-50625' to each side of the equation.
50625 + -2025x + -50625 + x2 = 0 + -50625

Reorder the terms:
50625 + -50625 + -2025x + x2 = 0 + -50625

Combine like terms: 50625 + -50625 = 0
0 + -2025x + x2 = 0 + -50625
-2025x + x2 = 0 + -50625

Combine like terms: 0 + -50625 = -50625
-2025x + x2 = -50625

The x term is -2025x.  Take half its coefficient (-1012.5).
Square it (1025156.25) and add it to both sides.

Add '1025156.25' to each side of the equation.
-2025x + 1025156.25 + x2 = -50625 + 1025156.25

Reorder the terms:
1025156.25 + -2025x + x2 = -50625 + 1025156.25

Combine like terms: -50625 + 1025156.25 = 974531.25
1025156.25 + -2025x + x2 = 974531.25

Factor a perfect square on the left side:
(x + -1012.5)(x + -1012.5) = 974531.25

Calculate the square root of the right side: 987.183493582

Break this problem into two subproblems by setting 
(x + -1012.5) equal to 987.183493582 and -987.183493582.


Subproblem 1
x + -1012.5 = 987.183493582

Simplifying
x + -1012.5 = 987.183493582

Reorder the terms:
-1012.5 + x = 987.183493582

Solving
-1012.5 + x = 987.183493582

Solving for variable 'x'.

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

Add '1012.5' to each side of the equation.
-1012.5 + 1012.5 + x = 987.183493582 + 1012.5

Combine like terms: -1012.5 + 1012.5 = 0.0
0.0 + x = 987.183493582 + 1012.5
x = 987.183493582 + 1012.5

Combine like terms: 987.183493582 + 1012.5 = 1999.683493582
x = 1999.683493582

Simplifying
x = 1999.683493582


Subproblem 2
x + -1012.5 = -987.183493582

Simplifying
x + -1012.5 = -987.183493582

Reorder the terms:
-1012.5 + x = -987.183493582

Solving
-1012.5 + x = -987.183493582

Solving for variable 'x'.

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

Add '1012.5' to each side of the equation.
-1012.5 + 1012.5 + x = -987.183493582 + 1012.5

Combine like terms: -1012.5 + 1012.5 = 0.0
0.0 + x = -987.183493582 + 1012.5
x = -987.183493582 + 1012.5

Combine like terms: -987.183493582 + 1012.5 = 25.316506418
x = 25.316506418

Simplifying
x = 25.316506418


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1999.683493582, 25.316506418}

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