x^2-.25x-64000=0

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Solution for x^2-.25x-64000=0 equation: 


Simplifying
x2 + -0.25x + -64000 = 0

Reorder the terms:
-64000 + -0.25x + x2 = 0

Solving
-64000 + -0.25x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '64000' to each side of the equation.
-64000 + -0.25x + 64000 + x2 = 0 + 64000

Reorder the terms:
-64000 + 64000 + -0.25x + x2 = 0 + 64000

Combine like terms: -64000 + 64000 = 0
0 + -0.25x + x2 = 0 + 64000
-0.25x + x2 = 0 + 64000

Combine like terms: 0 + 64000 = 64000
-0.25x + x2 = 64000

The x term is -0.25x.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25x + 0.015625 + x2 = 64000 + 0.015625

Reorder the terms:
0.015625 + -0.25x + x2 = 64000 + 0.015625

Combine like terms: 64000 + 0.015625 = 64000.015625
0.015625 + -0.25x + x2 = 64000.015625

Factor a perfect square on the left side:
(x + -0.125)(x + -0.125) = 64000.015625

Calculate the square root of the right side: 252.982243695

Break this problem into two subproblems by setting 
(x + -0.125) equal to 252.982243695 and -252.982243695.


Subproblem 1
x + -0.125 = 252.982243695

Simplifying
x + -0.125 = 252.982243695

Reorder the terms:
-0.125 + x = 252.982243695

Solving
-0.125 + x = 252.982243695

Solving for variable 'x'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + x = 252.982243695 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = 252.982243695 + 0.125
x = 252.982243695 + 0.125

Combine like terms: 252.982243695 + 0.125 = 253.107243695
x = 253.107243695

Simplifying
x = 253.107243695


Subproblem 2
x + -0.125 = -252.982243695

Simplifying
x + -0.125 = -252.982243695

Reorder the terms:
-0.125 + x = -252.982243695

Solving
-0.125 + x = -252.982243695

Solving for variable 'x'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + x = -252.982243695 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = -252.982243695 + 0.125
x = -252.982243695 + 0.125

Combine like terms: -252.982243695 + 0.125 = -252.857243695
x = -252.857243695

Simplifying
x = -252.857243695


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {253.107243695, -252.857243695}

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