4x^2-40000x+100=0

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Solution for 4x^2-40000x+100=0 equation: 


Simplifying
4x2 + -40000x + 100 = 0

Reorder the terms:
100 + -40000x + 4x2 = 0

Solving
100 + -40000x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(25 + -10000x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(25 + -10000x + x2)' equal to zero and attempt to solve:

Simplifying
25 + -10000x + x2 = 0

Solving
25 + -10000x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-25' to each side of the equation.
25 + -10000x + -25 + x2 = 0 + -25

Reorder the terms:
25 + -25 + -10000x + x2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -10000x + x2 = 0 + -25
-10000x + x2 = 0 + -25

Combine like terms: 0 + -25 = -25
-10000x + x2 = -25

The x term is -10000x.  Take half its coefficient (-5000).
Square it (25000000) and add it to both sides.

Add '25000000' to each side of the equation.
-10000x + 25000000 + x2 = -25 + 25000000

Reorder the terms:
25000000 + -10000x + x2 = -25 + 25000000

Combine like terms: -25 + 25000000 = 24999975
25000000 + -10000x + x2 = 24999975

Factor a perfect square on the left side:
(x + -5000)(x + -5000) = 24999975

Calculate the square root of the right side: 4999.997499999

Break this problem into two subproblems by setting 
(x + -5000) equal to 4999.997499999 and -4999.997499999.


Subproblem 1
x + -5000 = 4999.997499999

Simplifying
x + -5000 = 4999.997499999

Reorder the terms:
-5000 + x = 4999.997499999

Solving
-5000 + x = 4999.997499999

Solving for variable 'x'.

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

Add '5000' to each side of the equation.
-5000 + 5000 + x = 4999.997499999 + 5000

Combine like terms: -5000 + 5000 = 0
0 + x = 4999.997499999 + 5000
x = 4999.997499999 + 5000

Combine like terms: 4999.997499999 + 5000 = 9999.997499999
x = 9999.997499999

Simplifying
x = 9999.997499999


Subproblem 2
x + -5000 = -4999.997499999

Simplifying
x + -5000 = -4999.997499999

Reorder the terms:
-5000 + x = -4999.997499999

Solving
-5000 + x = -4999.997499999

Solving for variable 'x'.

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

Add '5000' to each side of the equation.
-5000 + 5000 + x = -4999.997499999 + 5000

Combine like terms: -5000 + 5000 = 0
0 + x = -4999.997499999 + 5000
x = -4999.997499999 + 5000

Combine like terms: -4999.997499999 + 5000 = 0.002500001
x = 0.002500001

Simplifying
x = 0.002500001


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9999.997499999, 0.002500001}
Solution
x = {9999.997499999, 0.002500001}

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