8n^2+92n-91=0

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Solution for 8n^2+92n-91=0 equation:


Simplifying
8n2 + 92n + -91 = 0

Reorder the terms:
-91 + 92n + 8n2 = 0

Solving
-91 + 92n + 8n2 = 0

Solving for variable 'n'.

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

Divide each side by '8'.
-11.375 + 11.5n + n2 = 0

Move the constant term to the right:

Add '11.375' to each side of the equation.
-11.375 + 11.5n + 11.375 + n2 = 0 + 11.375

Reorder the terms:
-11.375 + 11.375 + 11.5n + n2 = 0 + 11.375

Combine like terms: -11.375 + 11.375 = 0.000
0.000 + 11.5n + n2 = 0 + 11.375
11.5n + n2 = 0 + 11.375

Combine like terms: 0 + 11.375 = 11.375
11.5n + n2 = 11.375

The n term is 11.5n.  Take half its coefficient (5.75).
Square it (33.0625) and add it to both sides.

Add '33.0625' to each side of the equation.
11.5n + 33.0625 + n2 = 11.375 + 33.0625

Reorder the terms:
33.0625 + 11.5n + n2 = 11.375 + 33.0625

Combine like terms: 11.375 + 33.0625 = 44.4375
33.0625 + 11.5n + n2 = 44.4375

Factor a perfect square on the left side:
(n + 5.75)(n + 5.75) = 44.4375

Calculate the square root of the right side: 6.666145813

Break this problem into two subproblems by setting 
(n + 5.75) equal to 6.666145813 and -6.666145813.

Subproblem 1

n + 5.75 = 6.666145813 Simplifying n + 5.75 = 6.666145813 Reorder the terms: 5.75 + n = 6.666145813 Solving 5.75 + n = 6.666145813 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-5.75' to each side of the equation. 5.75 + -5.75 + n = 6.666145813 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + n = 6.666145813 + -5.75 n = 6.666145813 + -5.75 Combine like terms: 6.666145813 + -5.75 = 0.916145813 n = 0.916145813 Simplifying n = 0.916145813

Subproblem 2

n + 5.75 = -6.666145813 Simplifying n + 5.75 = -6.666145813 Reorder the terms: 5.75 + n = -6.666145813 Solving 5.75 + n = -6.666145813 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-5.75' to each side of the equation. 5.75 + -5.75 + n = -6.666145813 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + n = -6.666145813 + -5.75 n = -6.666145813 + -5.75 Combine like terms: -6.666145813 + -5.75 = -12.416145813 n = -12.416145813 Simplifying n = -12.416145813

Solution

The solution to the problem is based on the solutions from the subproblems. n = {0.916145813, -12.416145813}

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