n^2-18n+73=-3

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Solution for n^2-18n+73=-3 equation:


Simplifying
n2 + -18n + 73 = -3

Reorder the terms:
73 + -18n + n2 = -3

Solving
73 + -18n + n2 = -3

Solving for variable 'n'.

Reorder the terms:
73 + 3 + -18n + n2 = -3 + 3

Combine like terms: 73 + 3 = 76
76 + -18n + n2 = -3 + 3

Combine like terms: -3 + 3 = 0
76 + -18n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-76' to each side of the equation.
76 + -18n + -76 + n2 = 0 + -76

Reorder the terms:
76 + -76 + -18n + n2 = 0 + -76

Combine like terms: 76 + -76 = 0
0 + -18n + n2 = 0 + -76
-18n + n2 = 0 + -76

Combine like terms: 0 + -76 = -76
-18n + n2 = -76

The n term is -18n.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18n + 81 + n2 = -76 + 81

Reorder the terms:
81 + -18n + n2 = -76 + 81

Combine like terms: -76 + 81 = 5
81 + -18n + n2 = 5

Factor a perfect square on the left side:
(n + -9)(n + -9) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(n + -9) equal to 2.236067978 and -2.236067978.

Subproblem 1

n + -9 = 2.236067978 Simplifying n + -9 = 2.236067978 Reorder the terms: -9 + n = 2.236067978 Solving -9 + n = 2.236067978 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + n = 2.236067978 + 9 Combine like terms: -9 + 9 = 0 0 + n = 2.236067978 + 9 n = 2.236067978 + 9 Combine like terms: 2.236067978 + 9 = 11.236067978 n = 11.236067978 Simplifying n = 11.236067978

Subproblem 2

n + -9 = -2.236067978 Simplifying n + -9 = -2.236067978 Reorder the terms: -9 + n = -2.236067978 Solving -9 + n = -2.236067978 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + n = -2.236067978 + 9 Combine like terms: -9 + 9 = 0 0 + n = -2.236067978 + 9 n = -2.236067978 + 9 Combine like terms: -2.236067978 + 9 = 6.763932022 n = 6.763932022 Simplifying n = 6.763932022

Solution

The solution to the problem is based on the solutions from the subproblems. n = {11.236067978, 6.763932022}

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