N(N-1.2)=14

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Solution for N(N-1.2)=14 equation:


Simplifying
N(N + -1.2) = 14

Reorder the terms:
N(-1.2 + N) = 14
(-1.2 * N + N * N) = 14
(-1.2N + N2) = 14

Solving
-1.2N + N2 = 14

Solving for variable 'N'.

Reorder the terms:
-14 + -1.2N + N2 = 14 + -14

Combine like terms: 14 + -14 = 0
-14 + -1.2N + N2 = 0

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + -1.2N + 14 + N2 = 0 + 14

Reorder the terms:
-14 + 14 + -1.2N + N2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -1.2N + N2 = 0 + 14
-1.2N + N2 = 0 + 14

Combine like terms: 0 + 14 = 14
-1.2N + N2 = 14

The N term is -1.2N.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2N + 0.36 + N2 = 14 + 0.36

Reorder the terms:
0.36 + -1.2N + N2 = 14 + 0.36

Combine like terms: 14 + 0.36 = 14.36
0.36 + -1.2N + N2 = 14.36

Factor a perfect square on the left side:
(N + -0.6)(N + -0.6) = 14.36

Calculate the square root of the right side: 3.789459064

Break this problem into two subproblems by setting 
(N + -0.6) equal to 3.789459064 and -3.789459064.

Subproblem 1

N + -0.6 = 3.789459064 Simplifying N + -0.6 = 3.789459064 Reorder the terms: -0.6 + N = 3.789459064 Solving -0.6 + N = 3.789459064 Solving for variable 'N'. Move all terms containing N to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + N = 3.789459064 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + N = 3.789459064 + 0.6 N = 3.789459064 + 0.6 Combine like terms: 3.789459064 + 0.6 = 4.389459064 N = 4.389459064 Simplifying N = 4.389459064

Subproblem 2

N + -0.6 = -3.789459064 Simplifying N + -0.6 = -3.789459064 Reorder the terms: -0.6 + N = -3.789459064 Solving -0.6 + N = -3.789459064 Solving for variable 'N'. Move all terms containing N to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + N = -3.789459064 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + N = -3.789459064 + 0.6 N = -3.789459064 + 0.6 Combine like terms: -3.789459064 + 0.6 = -3.189459064 N = -3.189459064 Simplifying N = -3.189459064

Solution

The solution to the problem is based on the solutions from the subproblems. N = {4.389459064, -3.189459064}

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