x^2-95x+2000=0

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Solution for x^2-95x+2000=0 equation: 


Simplifying
x2 + -95x + 2000 = 0

Reorder the terms:
2000 + -95x + x2 = 0

Solving
2000 + -95x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2000' to each side of the equation.
2000 + -95x + -2000 + x2 = 0 + -2000

Reorder the terms:
2000 + -2000 + -95x + x2 = 0 + -2000

Combine like terms: 2000 + -2000 = 0
0 + -95x + x2 = 0 + -2000
-95x + x2 = 0 + -2000

Combine like terms: 0 + -2000 = -2000
-95x + x2 = -2000

The x term is -95x.  Take half its coefficient (-47.5).
Square it (2256.25) and add it to both sides.

Add '2256.25' to each side of the equation.
-95x + 2256.25 + x2 = -2000 + 2256.25

Reorder the terms:
2256.25 + -95x + x2 = -2000 + 2256.25

Combine like terms: -2000 + 2256.25 = 256.25
2256.25 + -95x + x2 = 256.25

Factor a perfect square on the left side:
(x + -47.5)(x + -47.5) = 256.25

Calculate the square root of the right side: 16.007810594

Break this problem into two subproblems by setting 
(x + -47.5) equal to 16.007810594 and -16.007810594.


Subproblem 1
x + -47.5 = 16.007810594

Simplifying
x + -47.5 = 16.007810594

Reorder the terms:
-47.5 + x = 16.007810594

Solving
-47.5 + x = 16.007810594

Solving for variable 'x'.

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

Add '47.5' to each side of the equation.
-47.5 + 47.5 + x = 16.007810594 + 47.5

Combine like terms: -47.5 + 47.5 = 0.0
0.0 + x = 16.007810594 + 47.5
x = 16.007810594 + 47.5

Combine like terms: 16.007810594 + 47.5 = 63.507810594
x = 63.507810594

Simplifying
x = 63.507810594


Subproblem 2
x + -47.5 = -16.007810594

Simplifying
x + -47.5 = -16.007810594

Reorder the terms:
-47.5 + x = -16.007810594

Solving
-47.5 + x = -16.007810594

Solving for variable 'x'.

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

Add '47.5' to each side of the equation.
-47.5 + 47.5 + x = -16.007810594 + 47.5

Combine like terms: -47.5 + 47.5 = 0.0
0.0 + x = -16.007810594 + 47.5
x = -16.007810594 + 47.5

Combine like terms: -16.007810594 + 47.5 = 31.492189406
x = 31.492189406

Simplifying
x = 31.492189406


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {63.507810594, 31.492189406}

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