3n^2+103n-100=0

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Solution for 3n^2+103n-100=0 equation: 


Simplifying
3n2 + 103n + -100 = 0

Reorder the terms:
-100 + 103n + 3n2 = 0

Solving
-100 + 103n + 3n2 = 0

Solving for variable 'n'.

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

Divide each side by '3'.
-33.33333333 + 34.33333333n + n2 = 0

Move the constant term to the right:

Add '33.33333333' to each side of the equation.
-33.33333333 + 34.33333333n + 33.33333333 + n2 = 0 + 33.33333333

Reorder the terms:
-33.33333333 + 33.33333333 + 34.33333333n + n2 = 0 + 33.33333333

Combine like terms: -33.33333333 + 33.33333333 = 0.00000000
0.00000000 + 34.33333333n + n2 = 0 + 33.33333333
34.33333333n + n2 = 0 + 33.33333333

Combine like terms: 0 + 33.33333333 = 33.33333333
34.33333333n + n2 = 33.33333333

The n term is 34.33333333n.  Take half its coefficient (17.16666667).
Square it (294.6944446) and add it to both sides.

Add '294.6944446' to each side of the equation.
34.33333333n + 294.6944446 + n2 = 33.33333333 + 294.6944446

Reorder the terms:
294.6944446 + 34.33333333n + n2 = 33.33333333 + 294.6944446

Combine like terms: 33.33333333 + 294.6944446 = 328.02777793
294.6944446 + 34.33333333n + n2 = 328.02777793

Factor a perfect square on the left side:
(n + 17.16666667)(n + 17.16666667) = 328.02777793

Calculate the square root of the right side: 18.11153715

Break this problem into two subproblems by setting 
(n + 17.16666667) equal to 18.11153715 and -18.11153715.


Subproblem 1
n + 17.16666667 = 18.11153715

Simplifying
n + 17.16666667 = 18.11153715

Reorder the terms:
17.16666667 + n = 18.11153715

Solving
17.16666667 + n = 18.11153715

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '-17.16666667' to each side of the equation.
17.16666667 + -17.16666667 + n = 18.11153715 + -17.16666667

Combine like terms: 17.16666667 + -17.16666667 = 0.00000000
0.00000000 + n = 18.11153715 + -17.16666667
n = 18.11153715 + -17.16666667

Combine like terms: 18.11153715 + -17.16666667 = 0.94487048
n = 0.94487048

Simplifying
n = 0.94487048


Subproblem 2
n + 17.16666667 = -18.11153715

Simplifying
n + 17.16666667 = -18.11153715

Reorder the terms:
17.16666667 + n = -18.11153715

Solving
17.16666667 + n = -18.11153715

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '-17.16666667' to each side of the equation.
17.16666667 + -17.16666667 + n = -18.11153715 + -17.16666667

Combine like terms: 17.16666667 + -17.16666667 = 0.00000000
0.00000000 + n = -18.11153715 + -17.16666667
n = -18.11153715 + -17.16666667

Combine like terms: -18.11153715 + -17.16666667 = -35.27820382
n = -35.27820382

Simplifying
n = -35.27820382


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.94487048, -35.27820382}

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