n^2-18n+18=-10

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Solution for n^2-18n+18=-10 equation:


Simplifying
n2 + -18n + 18 = -10

Reorder the terms:
18 + -18n + n2 = -10

Solving
18 + -18n + n2 = -10

Solving for variable 'n'.

Reorder the terms:
18 + 10 + -18n + n2 = -10 + 10

Combine like terms: 18 + 10 = 28
28 + -18n + n2 = -10 + 10

Combine like terms: -10 + 10 = 0
28 + -18n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-28' to each side of the equation.
28 + -18n + -28 + n2 = 0 + -28

Reorder the terms:
28 + -28 + -18n + n2 = 0 + -28

Combine like terms: 28 + -28 = 0
0 + -18n + n2 = 0 + -28
-18n + n2 = 0 + -28

Combine like terms: 0 + -28 = -28
-18n + n2 = -28

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 = -28 + 81

Reorder the terms:
81 + -18n + n2 = -28 + 81

Combine like terms: -28 + 81 = 53
81 + -18n + n2 = 53

Factor a perfect square on the left side:
(n + -9)(n + -9) = 53

Calculate the square root of the right side: 7.280109889

Break this problem into two subproblems by setting 
(n + -9) equal to 7.280109889 and -7.280109889.

Subproblem 1

n + -9 = 7.280109889 Simplifying n + -9 = 7.280109889 Reorder the terms: -9 + n = 7.280109889 Solving -9 + n = 7.280109889 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 = 7.280109889 + 9 Combine like terms: -9 + 9 = 0 0 + n = 7.280109889 + 9 n = 7.280109889 + 9 Combine like terms: 7.280109889 + 9 = 16.280109889 n = 16.280109889 Simplifying n = 16.280109889

Subproblem 2

n + -9 = -7.280109889 Simplifying n + -9 = -7.280109889 Reorder the terms: -9 + n = -7.280109889 Solving -9 + n = -7.280109889 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 = -7.280109889 + 9 Combine like terms: -9 + 9 = 0 0 + n = -7.280109889 + 9 n = -7.280109889 + 9 Combine like terms: -7.280109889 + 9 = 1.719890111 n = 1.719890111 Simplifying n = 1.719890111

Solution

The solution to the problem is based on the solutions from the subproblems. n = {16.280109889, 1.719890111}

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