n^2=-2-5n

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Solution for n^2=-2-5n equation: 


Simplifying
n2 = -2 + -5n

Solving
n2 = -2 + -5n

Solving for variable 'n'.

Reorder the terms:
2 + 5n + n2 = -2 + -5n + 2 + 5n

Reorder the terms:
2 + 5n + n2 = -2 + 2 + -5n + 5n

Combine like terms: -2 + 2 = 0
2 + 5n + n2 = 0 + -5n + 5n
2 + 5n + n2 = -5n + 5n

Combine like terms: -5n + 5n = 0
2 + 5n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 5n + -2 + n2 = 0 + -2

Reorder the terms:
2 + -2 + 5n + n2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5n + n2 = 0 + -2
5n + n2 = 0 + -2

Combine like terms: 0 + -2 = -2
5n + n2 = -2

The n term is 5n.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5n + 6.25 + n2 = -2 + 6.25

Reorder the terms:
6.25 + 5n + n2 = -2 + 6.25

Combine like terms: -2 + 6.25 = 4.25
6.25 + 5n + n2 = 4.25

Factor a perfect square on the left side:
(n + 2.5)(n + 2.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(n + 2.5) equal to 2.061552813 and -2.061552813.


Subproblem 1
n + 2.5 = 2.061552813

Simplifying
n + 2.5 = 2.061552813

Reorder the terms:
2.5 + n = 2.061552813

Solving
2.5 + n = 2.061552813

Solving for variable 'n'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + n = 2.061552813 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + n = 2.061552813 + -2.5
n = 2.061552813 + -2.5

Combine like terms: 2.061552813 + -2.5 = -0.438447187
n = -0.438447187

Simplifying
n = -0.438447187


Subproblem 2
n + 2.5 = -2.061552813

Simplifying
n + 2.5 = -2.061552813

Reorder the terms:
2.5 + n = -2.061552813

Solving
2.5 + n = -2.061552813

Solving for variable 'n'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + n = -2.061552813 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + n = -2.061552813 + -2.5
n = -2.061552813 + -2.5

Combine like terms: -2.061552813 + -2.5 = -4.561552813
n = -4.561552813

Simplifying
n = -4.561552813


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {-0.438447187, -4.561552813}

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