n(n+2)=1.0404

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Solution for n(n+2)=1.0404 equation:


Simplifying
n(n + 2) = 1.0404

Reorder the terms:
n(2 + n) = 1.0404
(2 * n + n * n) = 1.0404
(2n + n2) = 1.0404

Solving
2n + n2 = 1.0404

Solving for variable 'n'.

Reorder the terms:
-1.0404 + 2n + n2 = 1.0404 + -1.0404

Combine like terms: 1.0404 + -1.0404 = 0.0000
-1.0404 + 2n + n2 = 0.0000

Begin completing the square.

Move the constant term to the right:

Add '1.0404' to each side of the equation.
-1.0404 + 2n + 1.0404 + n2 = 0.0000 + 1.0404

Reorder the terms:
-1.0404 + 1.0404 + 2n + n2 = 0.0000 + 1.0404

Combine like terms: -1.0404 + 1.0404 = 0.0000
0.0000 + 2n + n2 = 0.0000 + 1.0404
2n + n2 = 0.0000 + 1.0404

Combine like terms: 0.0000 + 1.0404 = 1.0404
2n + n2 = 1.0404

The n term is 2n.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2n + 1 + n2 = 1.0404 + 1

Reorder the terms:
1 + 2n + n2 = 1.0404 + 1

Combine like terms: 1.0404 + 1 = 2.0404
1 + 2n + n2 = 2.0404

Factor a perfect square on the left side:
(n + 1)(n + 1) = 2.0404

Calculate the square root of the right side: 1.428425707

Break this problem into two subproblems by setting 
(n + 1) equal to 1.428425707 and -1.428425707.

Subproblem 1

n + 1 = 1.428425707 Simplifying n + 1 = 1.428425707 Reorder the terms: 1 + n = 1.428425707 Solving 1 + n = 1.428425707 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + n = 1.428425707 + -1 Combine like terms: 1 + -1 = 0 0 + n = 1.428425707 + -1 n = 1.428425707 + -1 Combine like terms: 1.428425707 + -1 = 0.428425707 n = 0.428425707 Simplifying n = 0.428425707

Subproblem 2

n + 1 = -1.428425707 Simplifying n + 1 = -1.428425707 Reorder the terms: 1 + n = -1.428425707 Solving 1 + n = -1.428425707 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + n = -1.428425707 + -1 Combine like terms: 1 + -1 = 0 0 + n = -1.428425707 + -1 n = -1.428425707 + -1 Combine like terms: -1.428425707 + -1 = -2.428425707 n = -2.428425707 Simplifying n = -2.428425707

Solution

The solution to the problem is based on the solutions from the subproblems. n = {0.428425707, -2.428425707}

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