x^2-2750x+3750=0

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Solution for x^2-2750x+3750=0 equation: 


Simplifying
x2 + -2750x + 3750 = 0

Reorder the terms:
3750 + -2750x + x2 = 0

Solving
3750 + -2750x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-3750' to each side of the equation.
3750 + -2750x + -3750 + x2 = 0 + -3750

Reorder the terms:
3750 + -3750 + -2750x + x2 = 0 + -3750

Combine like terms: 3750 + -3750 = 0
0 + -2750x + x2 = 0 + -3750
-2750x + x2 = 0 + -3750

Combine like terms: 0 + -3750 = -3750
-2750x + x2 = -3750

The x term is -2750x.  Take half its coefficient (-1375).
Square it (1890625) and add it to both sides.

Add '1890625' to each side of the equation.
-2750x + 1890625 + x2 = -3750 + 1890625

Reorder the terms:
1890625 + -2750x + x2 = -3750 + 1890625

Combine like terms: -3750 + 1890625 = 1886875
1890625 + -2750x + x2 = 1886875

Factor a perfect square on the left side:
(x + -1375)(x + -1375) = 1886875

Calculate the square root of the right side: 1373.635686782

Break this problem into two subproblems by setting 
(x + -1375) equal to 1373.635686782 and -1373.635686782.


Subproblem 1
x + -1375 = 1373.635686782

Simplifying
x + -1375 = 1373.635686782

Reorder the terms:
-1375 + x = 1373.635686782

Solving
-1375 + x = 1373.635686782

Solving for variable 'x'.

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

Add '1375' to each side of the equation.
-1375 + 1375 + x = 1373.635686782 + 1375

Combine like terms: -1375 + 1375 = 0
0 + x = 1373.635686782 + 1375
x = 1373.635686782 + 1375

Combine like terms: 1373.635686782 + 1375 = 2748.635686782
x = 2748.635686782

Simplifying
x = 2748.635686782


Subproblem 2
x + -1375 = -1373.635686782

Simplifying
x + -1375 = -1373.635686782

Reorder the terms:
-1375 + x = -1373.635686782

Solving
-1375 + x = -1373.635686782

Solving for variable 'x'.

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

Add '1375' to each side of the equation.
-1375 + 1375 + x = -1373.635686782 + 1375

Combine like terms: -1375 + 1375 = 0
0 + x = -1373.635686782 + 1375
x = -1373.635686782 + 1375

Combine like terms: -1373.635686782 + 1375 = 1.364313218
x = 1.364313218

Simplifying
x = 1.364313218


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2748.635686782, 1.364313218}

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