n^2=-18-10n

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


Simplifying
n2 = -18 + -10n

Solving
n2 = -18 + -10n

Solving for variable 'n'.

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

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

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

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

Begin completing the square.

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + 10n + -18 + n2 = 0 + -18

Reorder the terms:
18 + -18 + 10n + n2 = 0 + -18

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

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

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 = -18 + 25

Reorder the terms:
25 + 10n + n2 = -18 + 25

Combine like terms: -18 + 25 = 7
25 + 10n + n2 = 7

Factor a perfect square on the left side:
(n + 5)(n + 5) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(n + 5) equal to 2.645751311 and -2.645751311.

Subproblem 1

n + 5 = 2.645751311 Simplifying n + 5 = 2.645751311 Reorder the terms: 5 + n = 2.645751311 Solving 5 + n = 2.645751311 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 = 2.645751311 + -5 Combine like terms: 5 + -5 = 0 0 + n = 2.645751311 + -5 n = 2.645751311 + -5 Combine like terms: 2.645751311 + -5 = -2.354248689 n = -2.354248689 Simplifying n = -2.354248689

Subproblem 2

n + 5 = -2.645751311 Simplifying n + 5 = -2.645751311 Reorder the terms: 5 + n = -2.645751311 Solving 5 + n = -2.645751311 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 = -2.645751311 + -5 Combine like terms: 5 + -5 = 0 0 + n = -2.645751311 + -5 n = -2.645751311 + -5 Combine like terms: -2.645751311 + -5 = -7.645751311 n = -7.645751311 Simplifying n = -7.645751311

Solution

The solution to the problem is based on the solutions from the subproblems. n = {-2.354248689, -7.645751311}

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