n^2+4n-73=0

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Solution for n^2+4n-73=0 equation: 


Simplifying
n2 + 4n + -73 = 0

Reorder the terms:
-73 + 4n + n2 = 0

Solving
-73 + 4n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '73' to each side of the equation.
-73 + 4n + 73 + n2 = 0 + 73

Reorder the terms:
-73 + 73 + 4n + n2 = 0 + 73

Combine like terms: -73 + 73 = 0
0 + 4n + n2 = 0 + 73
4n + n2 = 0 + 73

Combine like terms: 0 + 73 = 73
4n + n2 = 73

The n term is 4n.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4n + 4 + n2 = 73 + 4

Reorder the terms:
4 + 4n + n2 = 73 + 4

Combine like terms: 73 + 4 = 77
4 + 4n + n2 = 77

Factor a perfect square on the left side:
(n + 2)(n + 2) = 77

Calculate the square root of the right side: 8.774964387

Break this problem into two subproblems by setting 
(n + 2) equal to 8.774964387 and -8.774964387.


Subproblem 1
n + 2 = 8.774964387

Simplifying
n + 2 = 8.774964387

Reorder the terms:
2 + n = 8.774964387

Solving
2 + n = 8.774964387

Solving for variable 'n'.

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

Add '-2' to each side of the equation.
2 + -2 + n = 8.774964387 + -2

Combine like terms: 2 + -2 = 0
0 + n = 8.774964387 + -2
n = 8.774964387 + -2

Combine like terms: 8.774964387 + -2 = 6.774964387
n = 6.774964387

Simplifying
n = 6.774964387


Subproblem 2
n + 2 = -8.774964387

Simplifying
n + 2 = -8.774964387

Reorder the terms:
2 + n = -8.774964387

Solving
2 + n = -8.774964387

Solving for variable 'n'.

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

Add '-2' to each side of the equation.
2 + -2 + n = -8.774964387 + -2

Combine like terms: 2 + -2 = 0
0 + n = -8.774964387 + -2
n = -8.774964387 + -2

Combine like terms: -8.774964387 + -2 = -10.774964387
n = -10.774964387

Simplifying
n = -10.774964387


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {6.774964387, -10.774964387}

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