3n^2+8n-350=0

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Solution for 3n^2+8n-350=0 equation: 


Simplifying
3n2 + 8n + -350 = 0

Reorder the terms:
-350 + 8n + 3n2 = 0

Solving
-350 + 8n + 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'.
-116.6666667 + 2.666666667n + n2 = 0

Move the constant term to the right:

Add '116.6666667' to each side of the equation.
-116.6666667 + 2.666666667n + 116.6666667 + n2 = 0 + 116.6666667

Reorder the terms:
-116.6666667 + 116.6666667 + 2.666666667n + n2 = 0 + 116.6666667

Combine like terms: -116.6666667 + 116.6666667 = 0.0000000
0.0000000 + 2.666666667n + n2 = 0 + 116.6666667
2.666666667n + n2 = 0 + 116.6666667

Combine like terms: 0 + 116.6666667 = 116.6666667
2.666666667n + n2 = 116.6666667

The n term is 2.666666667n.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667n + 1.777777780 + n2 = 116.6666667 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667n + n2 = 116.6666667 + 1.777777780

Combine like terms: 116.6666667 + 1.777777780 = 118.44444448
1.777777780 + 2.666666667n + n2 = 118.44444448

Factor a perfect square on the left side:
(n + 1.333333334)(n + 1.333333334) = 118.44444448

Calculate the square root of the right side: 10.88321848

Break this problem into two subproblems by setting 
(n + 1.333333334) equal to 10.88321848 and -10.88321848.


Subproblem 1
n + 1.333333334 = 10.88321848

Simplifying
n + 1.333333334 = 10.88321848

Reorder the terms:
1.333333334 + n = 10.88321848

Solving
1.333333334 + n = 10.88321848

Solving for variable 'n'.

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

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + n = 10.88321848 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + n = 10.88321848 + -1.333333334
n = 10.88321848 + -1.333333334

Combine like terms: 10.88321848 + -1.333333334 = 9.549885146
n = 9.549885146

Simplifying
n = 9.549885146


Subproblem 2
n + 1.333333334 = -10.88321848

Simplifying
n + 1.333333334 = -10.88321848

Reorder the terms:
1.333333334 + n = -10.88321848

Solving
1.333333334 + n = -10.88321848

Solving for variable 'n'.

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

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + n = -10.88321848 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + n = -10.88321848 + -1.333333334
n = -10.88321848 + -1.333333334

Combine like terms: -10.88321848 + -1.333333334 = -12.216551814
n = -12.216551814

Simplifying
n = -12.216551814


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {9.549885146, -12.216551814}

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