5n+5=n^2

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


Simplifying
5n + 5 = n2

Reorder the terms:
5 + 5n = n2

Solving
5 + 5n = n2

Solving for variable 'n'.

Combine like terms: n2 + -1n2 = 0
5 + 5n + -1n2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-5 + -5n + n2 = 0

Move the constant term to the right:

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

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

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

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

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 = 5 + 6.25

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

Combine like terms: 5 + 6.25 = 11.25
6.25 + -5n + n2 = 11.25

Factor a perfect square on the left side:
(n + -2.5)(n + -2.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(n + -2.5) equal to 3.354101966 and -3.354101966.

Subproblem 1

n + -2.5 = 3.354101966 Simplifying n + -2.5 = 3.354101966 Reorder the terms: -2.5 + n = 3.354101966 Solving -2.5 + n = 3.354101966 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 = 3.354101966 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + n = 3.354101966 + 2.5 n = 3.354101966 + 2.5 Combine like terms: 3.354101966 + 2.5 = 5.854101966 n = 5.854101966 Simplifying n = 5.854101966

Subproblem 2

n + -2.5 = -3.354101966 Simplifying n + -2.5 = -3.354101966 Reorder the terms: -2.5 + n = -3.354101966 Solving -2.5 + n = -3.354101966 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 = -3.354101966 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + n = -3.354101966 + 2.5 n = -3.354101966 + 2.5 Combine like terms: -3.354101966 + 2.5 = -0.854101966 n = -0.854101966 Simplifying n = -0.854101966

Solution

The solution to the problem is based on the solutions from the subproblems. n = {5.854101966, -0.854101966}

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