n^2+7n-92=0

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Solution for n^2+7n-92=0 equation:


Simplifying
n2 + 7n + -92 = 0

Reorder the terms:
-92 + 7n + n2 = 0

Solving
-92 + 7n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '92' to each side of the equation.
-92 + 7n + 92 + n2 = 0 + 92

Reorder the terms:
-92 + 92 + 7n + n2 = 0 + 92

Combine like terms: -92 + 92 = 0
0 + 7n + n2 = 0 + 92
7n + n2 = 0 + 92

Combine like terms: 0 + 92 = 92
7n + n2 = 92

The n term is 7n.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7n + 12.25 + n2 = 92 + 12.25

Reorder the terms:
12.25 + 7n + n2 = 92 + 12.25

Combine like terms: 92 + 12.25 = 104.25
12.25 + 7n + n2 = 104.25

Factor a perfect square on the left side:
(n + 3.5)(n + 3.5) = 104.25

Calculate the square root of the right side: 10.210288928

Break this problem into two subproblems by setting 
(n + 3.5) equal to 10.210288928 and -10.210288928.

Subproblem 1

n + 3.5 = 10.210288928 Simplifying n + 3.5 = 10.210288928 Reorder the terms: 3.5 + n = 10.210288928 Solving 3.5 + n = 10.210288928 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + n = 10.210288928 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + n = 10.210288928 + -3.5 n = 10.210288928 + -3.5 Combine like terms: 10.210288928 + -3.5 = 6.710288928 n = 6.710288928 Simplifying n = 6.710288928

Subproblem 2

n + 3.5 = -10.210288928 Simplifying n + 3.5 = -10.210288928 Reorder the terms: 3.5 + n = -10.210288928 Solving 3.5 + n = -10.210288928 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + n = -10.210288928 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + n = -10.210288928 + -3.5 n = -10.210288928 + -3.5 Combine like terms: -10.210288928 + -3.5 = -13.710288928 n = -13.710288928 Simplifying n = -13.710288928

Solution

The solution to the problem is based on the solutions from the subproblems. n = {6.710288928, -13.710288928}

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