n^2+n-200=0

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Solution for n^2+n-200=0 equation:


Simplifying
n2 + n + -200 = 0

Reorder the terms:
-200 + n + n2 = 0

Solving
-200 + n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '200' to each side of the equation.
-200 + n + 200 + n2 = 0 + 200

Reorder the terms:
-200 + 200 + n + n2 = 0 + 200

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

Combine like terms: 0 + 200 = 200
n + n2 = 200

The n term is n.  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.
n + 0.25 + n2 = 200 + 0.25

Reorder the terms:
0.25 + n + n2 = 200 + 0.25

Combine like terms: 200 + 0.25 = 200.25
0.25 + n + n2 = 200.25

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = 200.25

Calculate the square root of the right side: 14.150971698

Break this problem into two subproblems by setting 
(n + 0.5) equal to 14.150971698 and -14.150971698.

Subproblem 1

n + 0.5 = 14.150971698 Simplifying n + 0.5 = 14.150971698 Reorder the terms: 0.5 + n = 14.150971698 Solving 0.5 + n = 14.150971698 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 = 14.150971698 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 14.150971698 + -0.5 n = 14.150971698 + -0.5 Combine like terms: 14.150971698 + -0.5 = 13.650971698 n = 13.650971698 Simplifying n = 13.650971698

Subproblem 2

n + 0.5 = -14.150971698 Simplifying n + 0.5 = -14.150971698 Reorder the terms: 0.5 + n = -14.150971698 Solving 0.5 + n = -14.150971698 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 = -14.150971698 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -14.150971698 + -0.5 n = -14.150971698 + -0.5 Combine like terms: -14.150971698 + -0.5 = -14.650971698 n = -14.650971698 Simplifying n = -14.650971698

Solution

The solution to the problem is based on the solutions from the subproblems. n = {13.650971698, -14.650971698}

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