(n^2)-9n-94=8

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Solution for (n^2)-9n-94=8 equation:


Simplifying
(n2) + -9n + -94 = 8
n2 + -9n + -94 = 8

Reorder the terms:
-94 + -9n + n2 = 8

Solving
-94 + -9n + n2 = 8

Solving for variable 'n'.

Reorder the terms:
-94 + -8 + -9n + n2 = 8 + -8

Combine like terms: -94 + -8 = -102
-102 + -9n + n2 = 8 + -8

Combine like terms: 8 + -8 = 0
-102 + -9n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '102' to each side of the equation.
-102 + -9n + 102 + n2 = 0 + 102

Reorder the terms:
-102 + 102 + -9n + n2 = 0 + 102

Combine like terms: -102 + 102 = 0
0 + -9n + n2 = 0 + 102
-9n + n2 = 0 + 102

Combine like terms: 0 + 102 = 102
-9n + n2 = 102

The n term is -9n.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9n + 20.25 + n2 = 102 + 20.25

Reorder the terms:
20.25 + -9n + n2 = 102 + 20.25

Combine like terms: 102 + 20.25 = 122.25
20.25 + -9n + n2 = 122.25

Factor a perfect square on the left side:
(n + -4.5)(n + -4.5) = 122.25

Calculate the square root of the right side: 11.056672194

Break this problem into two subproblems by setting 
(n + -4.5) equal to 11.056672194 and -11.056672194.

Subproblem 1

n + -4.5 = 11.056672194 Simplifying n + -4.5 = 11.056672194 Reorder the terms: -4.5 + n = 11.056672194 Solving -4.5 + n = 11.056672194 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + n = 11.056672194 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + n = 11.056672194 + 4.5 n = 11.056672194 + 4.5 Combine like terms: 11.056672194 + 4.5 = 15.556672194 n = 15.556672194 Simplifying n = 15.556672194

Subproblem 2

n + -4.5 = -11.056672194 Simplifying n + -4.5 = -11.056672194 Reorder the terms: -4.5 + n = -11.056672194 Solving -4.5 + n = -11.056672194 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + n = -11.056672194 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + n = -11.056672194 + 4.5 n = -11.056672194 + 4.5 Combine like terms: -11.056672194 + 4.5 = -6.556672194 n = -6.556672194 Simplifying n = -6.556672194

Solution

The solution to the problem is based on the solutions from the subproblems. n = {15.556672194, -6.556672194}

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