n^2-n-5200=0

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Solution for n^2-n-5200=0 equation:


Simplifying
n2 + -1n + -5200 = 0

Reorder the terms:
-5200 + -1n + n2 = 0

Solving
-5200 + -1n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '5200' to each side of the equation.
-5200 + -1n + 5200 + n2 = 0 + 5200

Reorder the terms:
-5200 + 5200 + -1n + n2 = 0 + 5200

Combine like terms: -5200 + 5200 = 0
0 + -1n + n2 = 0 + 5200
-1n + n2 = 0 + 5200

Combine like terms: 0 + 5200 = 5200
-1n + n2 = 5200

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 = 5200 + 0.25

Reorder the terms:
0.25 + -1n + n2 = 5200 + 0.25

Combine like terms: 5200 + 0.25 = 5200.25
0.25 + -1n + n2 = 5200.25

Factor a perfect square on the left side:
(n + -0.5)(n + -0.5) = 5200.25

Calculate the square root of the right side: 72.112758927

Break this problem into two subproblems by setting 
(n + -0.5) equal to 72.112758927 and -72.112758927.

Subproblem 1

n + -0.5 = 72.112758927 Simplifying n + -0.5 = 72.112758927 Reorder the terms: -0.5 + n = 72.112758927 Solving -0.5 + n = 72.112758927 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 = 72.112758927 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = 72.112758927 + 0.5 n = 72.112758927 + 0.5 Combine like terms: 72.112758927 + 0.5 = 72.612758927 n = 72.612758927 Simplifying n = 72.612758927

Subproblem 2

n + -0.5 = -72.112758927 Simplifying n + -0.5 = -72.112758927 Reorder the terms: -0.5 + n = -72.112758927 Solving -0.5 + n = -72.112758927 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 = -72.112758927 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = -72.112758927 + 0.5 n = -72.112758927 + 0.5 Combine like terms: -72.112758927 + 0.5 = -71.612758927 n = -71.612758927 Simplifying n = -71.612758927

Solution

The solution to the problem is based on the solutions from the subproblems. n = {72.612758927, -71.612758927}

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