9x^2+3x-92=0

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Solution for 9x^2+3x-92=0 equation: 


Simplifying
9x2 + 3x + -92 = 0

Reorder the terms:
-92 + 3x + 9x2 = 0

Solving
-92 + 3x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
-10.22222222 + 0.3333333333x + x2 = 0

Move the constant term to the right:

Add '10.22222222' to each side of the equation.
-10.22222222 + 0.3333333333x + 10.22222222 + x2 = 0 + 10.22222222

Reorder the terms:
-10.22222222 + 10.22222222 + 0.3333333333x + x2 = 0 + 10.22222222

Combine like terms: -10.22222222 + 10.22222222 = 0.00000000
0.00000000 + 0.3333333333x + x2 = 0 + 10.22222222
0.3333333333x + x2 = 0 + 10.22222222

Combine like terms: 0 + 10.22222222 = 10.22222222
0.3333333333x + x2 = 10.22222222

The x term is 0.3333333333x.  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.
0.3333333333x + 0.02777777779 + x2 = 10.22222222 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333x + x2 = 10.22222222 + 0.02777777779

Combine like terms: 10.22222222 + 0.02777777779 = 10.24999999779
0.02777777779 + 0.3333333333x + x2 = 10.24999999779

Factor a perfect square on the left side:
(x + 0.1666666667)(x + 0.1666666667) = 10.24999999779

Calculate the square root of the right side: 3.201562118

Break this problem into two subproblems by setting 
(x + 0.1666666667) equal to 3.201562118 and -3.201562118.


Subproblem 1
x + 0.1666666667 = 3.201562118

Simplifying
x + 0.1666666667 = 3.201562118

Reorder the terms:
0.1666666667 + x = 3.201562118

Solving
0.1666666667 + x = 3.201562118

Solving for variable 'x'.

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

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + x = 3.201562118 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + x = 3.201562118 + -0.1666666667
x = 3.201562118 + -0.1666666667

Combine like terms: 3.201562118 + -0.1666666667 = 3.0348954513
x = 3.0348954513

Simplifying
x = 3.0348954513


Subproblem 2
x + 0.1666666667 = -3.201562118

Simplifying
x + 0.1666666667 = -3.201562118

Reorder the terms:
0.1666666667 + x = -3.201562118

Solving
0.1666666667 + x = -3.201562118

Solving for variable 'x'.

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

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + x = -3.201562118 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + x = -3.201562118 + -0.1666666667
x = -3.201562118 + -0.1666666667

Combine like terms: -3.201562118 + -0.1666666667 = -3.3682287847
x = -3.3682287847

Simplifying
x = -3.3682287847


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.0348954513, -3.3682287847}

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