5n^2-129n-729=0

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Solution for 5n^2-129n-729=0 equation:


Simplifying
5n2 + -129n + -729 = 0

Reorder the terms:
-729 + -129n + 5n2 = 0

Solving
-729 + -129n + 5n2 = 0

Solving for variable 'n'.

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

Divide each side by '5'.
-145.8 + -25.8n + n2 = 0

Move the constant term to the right:

Add '145.8' to each side of the equation.
-145.8 + -25.8n + 145.8 + n2 = 0 + 145.8

Reorder the terms:
-145.8 + 145.8 + -25.8n + n2 = 0 + 145.8

Combine like terms: -145.8 + 145.8 = 0.0
0.0 + -25.8n + n2 = 0 + 145.8
-25.8n + n2 = 0 + 145.8

Combine like terms: 0 + 145.8 = 145.8
-25.8n + n2 = 145.8

The n term is -25.8n.  Take half its coefficient (-12.9).
Square it (166.41) and add it to both sides.

Add '166.41' to each side of the equation.
-25.8n + 166.41 + n2 = 145.8 + 166.41

Reorder the terms:
166.41 + -25.8n + n2 = 145.8 + 166.41

Combine like terms: 145.8 + 166.41 = 312.21
166.41 + -25.8n + n2 = 312.21

Factor a perfect square on the left side:
(n + -12.9)(n + -12.9) = 312.21

Calculate the square root of the right side: 17.669465187

Break this problem into two subproblems by setting 
(n + -12.9) equal to 17.669465187 and -17.669465187.

Subproblem 1

n + -12.9 = 17.669465187 Simplifying n + -12.9 = 17.669465187 Reorder the terms: -12.9 + n = 17.669465187 Solving -12.9 + n = 17.669465187 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '12.9' to each side of the equation. -12.9 + 12.9 + n = 17.669465187 + 12.9 Combine like terms: -12.9 + 12.9 = 0.0 0.0 + n = 17.669465187 + 12.9 n = 17.669465187 + 12.9 Combine like terms: 17.669465187 + 12.9 = 30.569465187 n = 30.569465187 Simplifying n = 30.569465187

Subproblem 2

n + -12.9 = -17.669465187 Simplifying n + -12.9 = -17.669465187 Reorder the terms: -12.9 + n = -17.669465187 Solving -12.9 + n = -17.669465187 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '12.9' to each side of the equation. -12.9 + 12.9 + n = -17.669465187 + 12.9 Combine like terms: -12.9 + 12.9 = 0.0 0.0 + n = -17.669465187 + 12.9 n = -17.669465187 + 12.9 Combine like terms: -17.669465187 + 12.9 = -4.769465187 n = -4.769465187 Simplifying n = -4.769465187

Solution

The solution to the problem is based on the solutions from the subproblems. n = {30.569465187, -4.769465187}

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