n(n+14)=-3

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Solution for n(n+14)=-3 equation:


Simplifying
n(n + 14) = -3

Reorder the terms:
n(14 + n) = -3
(14 * n + n * n) = -3
(14n + n2) = -3

Solving
14n + n2 = -3

Solving for variable 'n'.

Reorder the terms:
3 + 14n + n2 = -3 + 3

Combine like terms: -3 + 3 = 0
3 + 14n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 14n + -3 + n2 = 0 + -3

Reorder the terms:
3 + -3 + 14n + n2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 14n + n2 = 0 + -3
14n + n2 = 0 + -3

Combine like terms: 0 + -3 = -3
14n + n2 = -3

The n term is 14n.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14n + 49 + n2 = -3 + 49

Reorder the terms:
49 + 14n + n2 = -3 + 49

Combine like terms: -3 + 49 = 46
49 + 14n + n2 = 46

Factor a perfect square on the left side:
(n + 7)(n + 7) = 46

Calculate the square root of the right side: 6.782329983

Break this problem into two subproblems by setting 
(n + 7) equal to 6.782329983 and -6.782329983.

Subproblem 1

n + 7 = 6.782329983 Simplifying n + 7 = 6.782329983 Reorder the terms: 7 + n = 6.782329983 Solving 7 + n = 6.782329983 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + n = 6.782329983 + -7 Combine like terms: 7 + -7 = 0 0 + n = 6.782329983 + -7 n = 6.782329983 + -7 Combine like terms: 6.782329983 + -7 = -0.217670017 n = -0.217670017 Simplifying n = -0.217670017

Subproblem 2

n + 7 = -6.782329983 Simplifying n + 7 = -6.782329983 Reorder the terms: 7 + n = -6.782329983 Solving 7 + n = -6.782329983 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + n = -6.782329983 + -7 Combine like terms: 7 + -7 = 0 0 + n = -6.782329983 + -7 n = -6.782329983 + -7 Combine like terms: -6.782329983 + -7 = -13.782329983 n = -13.782329983 Simplifying n = -13.782329983

Solution

The solution to the problem is based on the solutions from the subproblems. n = {-0.217670017, -13.782329983}

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