x^2-875x+15625=0

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Solution for x^2-875x+15625=0 equation: 


Simplifying
x2 + -875x + 15625 = 0

Reorder the terms:
15625 + -875x + x2 = 0

Solving
15625 + -875x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-15625' to each side of the equation.
15625 + -875x + -15625 + x2 = 0 + -15625

Reorder the terms:
15625 + -15625 + -875x + x2 = 0 + -15625

Combine like terms: 15625 + -15625 = 0
0 + -875x + x2 = 0 + -15625
-875x + x2 = 0 + -15625

Combine like terms: 0 + -15625 = -15625
-875x + x2 = -15625

The x term is -875x.  Take half its coefficient (-437.5).
Square it (191406.25) and add it to both sides.

Add '191406.25' to each side of the equation.
-875x + 191406.25 + x2 = -15625 + 191406.25

Reorder the terms:
191406.25 + -875x + x2 = -15625 + 191406.25

Combine like terms: -15625 + 191406.25 = 175781.25
191406.25 + -875x + x2 = 175781.25

Factor a perfect square on the left side:
(x + -437.5)(x + -437.5) = 175781.25

Calculate the square root of the right side: 419.262745781

Break this problem into two subproblems by setting 
(x + -437.5) equal to 419.262745781 and -419.262745781.


Subproblem 1
x + -437.5 = 419.262745781

Simplifying
x + -437.5 = 419.262745781

Reorder the terms:
-437.5 + x = 419.262745781

Solving
-437.5 + x = 419.262745781

Solving for variable 'x'.

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

Add '437.5' to each side of the equation.
-437.5 + 437.5 + x = 419.262745781 + 437.5

Combine like terms: -437.5 + 437.5 = 0.0
0.0 + x = 419.262745781 + 437.5
x = 419.262745781 + 437.5

Combine like terms: 419.262745781 + 437.5 = 856.762745781
x = 856.762745781

Simplifying
x = 856.762745781


Subproblem 2
x + -437.5 = -419.262745781

Simplifying
x + -437.5 = -419.262745781

Reorder the terms:
-437.5 + x = -419.262745781

Solving
-437.5 + x = -419.262745781

Solving for variable 'x'.

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

Add '437.5' to each side of the equation.
-437.5 + 437.5 + x = -419.262745781 + 437.5

Combine like terms: -437.5 + 437.5 = 0.0
0.0 + x = -419.262745781 + 437.5
x = -419.262745781 + 437.5

Combine like terms: -419.262745781 + 437.5 = 18.237254219
x = 18.237254219

Simplifying
x = 18.237254219


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {856.762745781, 18.237254219}

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