9n^2+3n-10=

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Solution for 9n^2+3n-10= equation: 


Simplifying
9n2 + 3n + -10 = 0

Reorder the terms:
-10 + 3n + 9n2 = 0

Solving
-10 + 3n + 9n2 = 0

Solving for variable 'n'.

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

Divide each side by '9'.
-1.111111111 + 0.3333333333n + n2 = 0

Move the constant term to the right:

Add '1.111111111' to each side of the equation.
-1.111111111 + 0.3333333333n + 1.111111111 + n2 = 0 + 1.111111111

Reorder the terms:
-1.111111111 + 1.111111111 + 0.3333333333n + n2 = 0 + 1.111111111

Combine like terms: -1.111111111 + 1.111111111 = 0.000000000
0.000000000 + 0.3333333333n + n2 = 0 + 1.111111111
0.3333333333n + n2 = 0 + 1.111111111

Combine like terms: 0 + 1.111111111 = 1.111111111
0.3333333333n + n2 = 1.111111111

The n term is 0.3333333333n.  Take half its coefficient (0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
0.3333333333n + 0.02777777779 + n2 = 1.111111111 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333n + n2 = 1.111111111 + 0.02777777779

Combine like terms: 1.111111111 + 0.02777777779 = 1.13888888879
0.02777777779 + 0.3333333333n + n2 = 1.13888888879

Factor a perfect square on the left side:
(n + 0.1666666667)(n + 0.1666666667) = 1.13888888879

Calculate the square root of the right side: 1.067187373

Break this problem into two subproblems by setting 
(n + 0.1666666667) equal to 1.067187373 and -1.067187373.


Subproblem 1
n + 0.1666666667 = 1.067187373

Simplifying
n + 0.1666666667 = 1.067187373

Reorder the terms:
0.1666666667 + n = 1.067187373

Solving
0.1666666667 + n = 1.067187373

Solving for variable 'n'.

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

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + n = 1.067187373 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + n = 1.067187373 + -0.1666666667
n = 1.067187373 + -0.1666666667

Combine like terms: 1.067187373 + -0.1666666667 = 0.9005207063
n = 0.9005207063

Simplifying
n = 0.9005207063


Subproblem 2
n + 0.1666666667 = -1.067187373

Simplifying
n + 0.1666666667 = -1.067187373

Reorder the terms:
0.1666666667 + n = -1.067187373

Solving
0.1666666667 + n = -1.067187373

Solving for variable 'n'.

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

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + n = -1.067187373 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + n = -1.067187373 + -0.1666666667
n = -1.067187373 + -0.1666666667

Combine like terms: -1.067187373 + -0.1666666667 = -1.2338540397
n = -1.2338540397

Simplifying
n = -1.2338540397


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.9005207063, -1.2338540397}

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