N*(5+N)=26.24

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Solution for N*(5+N)=26.24 equation: 


Simplifying
N(5 + N) = 26.24
(5 * N + N * N) = 26.24
(5N + N2) = 26.24

Solving
5N + N2 = 26.24

Solving for variable 'N'.

Reorder the terms:
-26.24 + 5N + N2 = 26.24 + -26.24

Combine like terms: 26.24 + -26.24 = 0.00
-26.24 + 5N + N2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '26.24' to each side of the equation.
-26.24 + 5N + 26.24 + N2 = 0.00 + 26.24

Reorder the terms:
-26.24 + 26.24 + 5N + N2 = 0.00 + 26.24

Combine like terms: -26.24 + 26.24 = 0.00
0.00 + 5N + N2 = 0.00 + 26.24
5N + N2 = 0.00 + 26.24

Combine like terms: 0.00 + 26.24 = 26.24
5N + N2 = 26.24

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 = 26.24 + 6.25

Reorder the terms:
6.25 + 5N + N2 = 26.24 + 6.25

Combine like terms: 26.24 + 6.25 = 32.49
6.25 + 5N + N2 = 32.49

Factor a perfect square on the left side:
(N + 2.5)(N + 2.5) = 32.49

Calculate the square root of the right side: 5.7

Break this problem into two subproblems by setting 
(N + 2.5) equal to 5.7 and -5.7.


Subproblem 1
N + 2.5 = 5.7

Simplifying
N + 2.5 = 5.7

Reorder the terms:
2.5 + N = 5.7

Solving
2.5 + N = 5.7

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 = 5.7 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + N = 5.7 + -2.5
N = 5.7 + -2.5

Combine like terms: 5.7 + -2.5 = 3.2
N = 3.2

Simplifying
N = 3.2


Subproblem 2
N + 2.5 = -5.7

Simplifying
N + 2.5 = -5.7

Reorder the terms:
2.5 + N = -5.7

Solving
2.5 + N = -5.7

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 = -5.7 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + N = -5.7 + -2.5
N = -5.7 + -2.5

Combine like terms: -5.7 + -2.5 = -8.2
N = -8.2

Simplifying
N = -8.2


Solution
The solution to the problem is based on the solutions
from the subproblems.
N = {3.2, -8.2}

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