2000+-91.93548387x+x^2=0

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Solution for 2000+-91.93548387x+x^2=0 equation: 


Simplifying
2000 + -91.93548387x + x2 = 0

Solving
2000 + -91.93548387x + 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 + -91.93548387x + -2000 + x2 = 0 + -2000

Reorder the terms:
2000 + -2000 + -91.93548387x + x2 = 0 + -2000

Combine like terms: 2000 + -2000 = 0
0 + -91.93548387x + x2 = 0 + -2000
-91.93548387x + x2 = 0 + -2000

Combine like terms: 0 + -2000 = -2000
-91.93548387x + x2 = -2000

The x term is -91.93548387x.  Take half its coefficient (-45.96774194).
Square it (2113.033299) and add it to both sides.

Add '2113.033299' to each side of the equation.
-91.93548387x + 2113.033299 + x2 = -2000 + 2113.033299

Reorder the terms:
2113.033299 + -91.93548387x + x2 = -2000 + 2113.033299

Combine like terms: -2000 + 2113.033299 = 113.033299
2113.033299 + -91.93548387x + x2 = 113.033299

Factor a perfect square on the left side:
(x + -45.96774194)(x + -45.96774194) = 113.033299

Calculate the square root of the right side: 10.631711951

Break this problem into two subproblems by setting 
(x + -45.96774194) equal to 10.631711951 and -10.631711951.


Subproblem 1
x + -45.96774194 = 10.631711951

Simplifying
x + -45.96774194 = 10.631711951

Reorder the terms:
-45.96774194 + x = 10.631711951

Solving
-45.96774194 + x = 10.631711951

Solving for variable 'x'.

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

Add '45.96774194' to each side of the equation.
-45.96774194 + 45.96774194 + x = 10.631711951 + 45.96774194

Combine like terms: -45.96774194 + 45.96774194 = 0.00000000
0.00000000 + x = 10.631711951 + 45.96774194
x = 10.631711951 + 45.96774194

Combine like terms: 10.631711951 + 45.96774194 = 56.599453891
x = 56.599453891

Simplifying
x = 56.599453891


Subproblem 2
x + -45.96774194 = -10.631711951

Simplifying
x + -45.96774194 = -10.631711951

Reorder the terms:
-45.96774194 + x = -10.631711951

Solving
-45.96774194 + x = -10.631711951

Solving for variable 'x'.

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

Add '45.96774194' to each side of the equation.
-45.96774194 + 45.96774194 + x = -10.631711951 + 45.96774194

Combine like terms: -45.96774194 + 45.96774194 = 0.00000000
0.00000000 + x = -10.631711951 + 45.96774194
x = -10.631711951 + 45.96774194

Combine like terms: -10.631711951 + 45.96774194 = 35.336029989
x = 35.336029989

Simplifying
x = 35.336029989


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {56.599453891, 35.336029989}

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