n^2-10n-88=-5

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Solution for n^2-10n-88=-5 equation:


Simplifying
n2 + -10n + -88 = -5

Reorder the terms:
-88 + -10n + n2 = -5

Solving
-88 + -10n + n2 = -5

Solving for variable 'n'.

Reorder the terms:
-88 + 5 + -10n + n2 = -5 + 5

Combine like terms: -88 + 5 = -83
-83 + -10n + n2 = -5 + 5

Combine like terms: -5 + 5 = 0
-83 + -10n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '83' to each side of the equation.
-83 + -10n + 83 + n2 = 0 + 83

Reorder the terms:
-83 + 83 + -10n + n2 = 0 + 83

Combine like terms: -83 + 83 = 0
0 + -10n + n2 = 0 + 83
-10n + n2 = 0 + 83

Combine like terms: 0 + 83 = 83
-10n + n2 = 83

The n term is -10n.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10n + 25 + n2 = 83 + 25

Reorder the terms:
25 + -10n + n2 = 83 + 25

Combine like terms: 83 + 25 = 108
25 + -10n + n2 = 108

Factor a perfect square on the left side:
(n + -5)(n + -5) = 108

Calculate the square root of the right side: 10.392304845

Break this problem into two subproblems by setting 
(n + -5) equal to 10.392304845 and -10.392304845.

Subproblem 1

n + -5 = 10.392304845 Simplifying n + -5 = 10.392304845 Reorder the terms: -5 + n = 10.392304845 Solving -5 + n = 10.392304845 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + n = 10.392304845 + 5 Combine like terms: -5 + 5 = 0 0 + n = 10.392304845 + 5 n = 10.392304845 + 5 Combine like terms: 10.392304845 + 5 = 15.392304845 n = 15.392304845 Simplifying n = 15.392304845

Subproblem 2

n + -5 = -10.392304845 Simplifying n + -5 = -10.392304845 Reorder the terms: -5 + n = -10.392304845 Solving -5 + n = -10.392304845 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + n = -10.392304845 + 5 Combine like terms: -5 + 5 = 0 0 + n = -10.392304845 + 5 n = -10.392304845 + 5 Combine like terms: -10.392304845 + 5 = -5.392304845 n = -5.392304845 Simplifying n = -5.392304845

Solution

The solution to the problem is based on the solutions from the subproblems. n = {15.392304845, -5.392304845}

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