-2=-n(n+8)

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Solution for -2=-n(n+8) equation:


Simplifying
-2 = -1n(n + 8)

Reorder the terms:
-2 = -1n(8 + n)
-2 = (8 * -1n + n * -1n)
-2 = (-8n + -1n2)

Solving
-2 = -8n + -1n2

Solving for variable 'n'.

Reorder the terms:
-2 + 8n + n2 = -8n + 8n + -1n2 + n2

Combine like terms: -8n + 8n = 0
-2 + 8n + n2 = 0 + -1n2 + n2
-2 + 8n + n2 = -1n2 + n2

Combine like terms: -1n2 + n2 = 0
-2 + 8n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 8n + 2 + n2 = 0 + 2

Reorder the terms:
-2 + 2 + 8n + n2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 8n + n2 = 0 + 2
8n + n2 = 0 + 2

Combine like terms: 0 + 2 = 2
8n + n2 = 2

The n term is 8n.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8n + 16 + n2 = 2 + 16

Reorder the terms:
16 + 8n + n2 = 2 + 16

Combine like terms: 2 + 16 = 18
16 + 8n + n2 = 18

Factor a perfect square on the left side:
(n + 4)(n + 4) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(n + 4) equal to 4.242640687 and -4.242640687.

Subproblem 1

n + 4 = 4.242640687 Simplifying n + 4 = 4.242640687 Reorder the terms: 4 + n = 4.242640687 Solving 4 + n = 4.242640687 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + n = 4.242640687 + -4 Combine like terms: 4 + -4 = 0 0 + n = 4.242640687 + -4 n = 4.242640687 + -4 Combine like terms: 4.242640687 + -4 = 0.242640687 n = 0.242640687 Simplifying n = 0.242640687

Subproblem 2

n + 4 = -4.242640687 Simplifying n + 4 = -4.242640687 Reorder the terms: 4 + n = -4.242640687 Solving 4 + n = -4.242640687 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + n = -4.242640687 + -4 Combine like terms: 4 + -4 = 0 0 + n = -4.242640687 + -4 n = -4.242640687 + -4 Combine like terms: -4.242640687 + -4 = -8.242640687 n = -8.242640687 Simplifying n = -8.242640687

Solution

The solution to the problem is based on the solutions from the subproblems. n = {0.242640687, -8.242640687}

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