n^2-n+2.5=200

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Solution for n^2-n+2.5=200 equation: 


Simplifying
n2 + -1n + 2.5 = 200

Reorder the terms:
2.5 + -1n + n2 = 200

Solving
2.5 + -1n + n2 = 200

Solving for variable 'n'.

Reorder the terms:
2.5 + -200 + -1n + n2 = 200 + -200

Combine like terms: 2.5 + -200 = -197.5
-197.5 + -1n + n2 = 200 + -200

Combine like terms: 200 + -200 = 0
-197.5 + -1n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '197.5' to each side of the equation.
-197.5 + -1n + 197.5 + n2 = 0 + 197.5

Reorder the terms:
-197.5 + 197.5 + -1n + n2 = 0 + 197.5

Combine like terms: -197.5 + 197.5 = 0.0
0.0 + -1n + n2 = 0 + 197.5
-1n + n2 = 0 + 197.5

Combine like terms: 0 + 197.5 = 197.5
-1n + n2 = 197.5

The n term is -1n.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1n + 0.25 + n2 = 197.5 + 0.25

Reorder the terms:
0.25 + -1n + n2 = 197.5 + 0.25

Combine like terms: 197.5 + 0.25 = 197.75
0.25 + -1n + n2 = 197.75

Factor a perfect square on the left side:
(n + -0.5)(n + -0.5) = 197.75

Calculate the square root of the right side: 14.06236111

Break this problem into two subproblems by setting 
(n + -0.5) equal to 14.06236111 and -14.06236111.


Subproblem 1
n + -0.5 = 14.06236111

Simplifying
n + -0.5 = 14.06236111

Reorder the terms:
-0.5 + n = 14.06236111

Solving
-0.5 + n = 14.06236111

Solving for variable 'n'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + n = 14.06236111 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + n = 14.06236111 + 0.5
n = 14.06236111 + 0.5

Combine like terms: 14.06236111 + 0.5 = 14.56236111
n = 14.56236111

Simplifying
n = 14.56236111


Subproblem 2
n + -0.5 = -14.06236111

Simplifying
n + -0.5 = -14.06236111

Reorder the terms:
-0.5 + n = -14.06236111

Solving
-0.5 + n = -14.06236111

Solving for variable 'n'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + n = -14.06236111 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + n = -14.06236111 + 0.5
n = -14.06236111 + 0.5

Combine like terms: -14.06236111 + 0.5 = -13.56236111
n = -13.56236111

Simplifying
n = -13.56236111


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {14.56236111, -13.56236111}

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