0=n^2+14n-60

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Solution for 0=n^2+14n-60 equation:


Simplifying
0 = n2 + 14n + -60

Reorder the terms:
0 = -60 + 14n + n2

Solving
0 = -60 + 14n + n2

Solving for variable 'n'.

Combine like terms: 0 + 60 = 60
60 + -14n + -1n2 = -60 + 14n + n2 + 60 + -14n + -1n2

Reorder the terms:
60 + -14n + -1n2 = -60 + 60 + 14n + -14n + n2 + -1n2

Combine like terms: -60 + 60 = 0
60 + -14n + -1n2 = 0 + 14n + -14n + n2 + -1n2
60 + -14n + -1n2 = 14n + -14n + n2 + -1n2

Combine like terms: 14n + -14n = 0
60 + -14n + -1n2 = 0 + n2 + -1n2
60 + -14n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
60 + -14n + -1n2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-60 + 14n + n2 = 0

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + 14n + 60 + n2 = 0 + 60

Reorder the terms:
-60 + 60 + 14n + n2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + 14n + n2 = 0 + 60
14n + n2 = 0 + 60

Combine like terms: 0 + 60 = 60
14n + n2 = 60

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 = 60 + 49

Reorder the terms:
49 + 14n + n2 = 60 + 49

Combine like terms: 60 + 49 = 109
49 + 14n + n2 = 109

Factor a perfect square on the left side:
(n + 7)(n + 7) = 109

Calculate the square root of the right side: 10.440306509

Break this problem into two subproblems by setting 
(n + 7) equal to 10.440306509 and -10.440306509.

Subproblem 1

n + 7 = 10.440306509 Simplifying n + 7 = 10.440306509 Reorder the terms: 7 + n = 10.440306509 Solving 7 + n = 10.440306509 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 = 10.440306509 + -7 Combine like terms: 7 + -7 = 0 0 + n = 10.440306509 + -7 n = 10.440306509 + -7 Combine like terms: 10.440306509 + -7 = 3.440306509 n = 3.440306509 Simplifying n = 3.440306509

Subproblem 2

n + 7 = -10.440306509 Simplifying n + 7 = -10.440306509 Reorder the terms: 7 + n = -10.440306509 Solving 7 + n = -10.440306509 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 = -10.440306509 + -7 Combine like terms: 7 + -7 = 0 0 + n = -10.440306509 + -7 n = -10.440306509 + -7 Combine like terms: -10.440306509 + -7 = -17.440306509 n = -17.440306509 Simplifying n = -17.440306509

Solution

The solution to the problem is based on the solutions from the subproblems. n = {3.440306509, -17.440306509}

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