x^2+9x-184=0

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Solution for x^2+9x-184=0 equation: 


Simplifying
x2 + 9x + -184 = 0

Reorder the terms:
-184 + 9x + x2 = 0

Solving
-184 + 9x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '184' to each side of the equation.
-184 + 9x + 184 + x2 = 0 + 184

Reorder the terms:
-184 + 184 + 9x + x2 = 0 + 184

Combine like terms: -184 + 184 = 0
0 + 9x + x2 = 0 + 184
9x + x2 = 0 + 184

Combine like terms: 0 + 184 = 184
9x + x2 = 184

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = 184 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 184 + 20.25

Combine like terms: 184 + 20.25 = 204.25
20.25 + 9x + x2 = 204.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 204.25

Calculate the square root of the right side: 14.291605928

Break this problem into two subproblems by setting 
(x + 4.5) equal to 14.291605928 and -14.291605928.


Subproblem 1
x + 4.5 = 14.291605928

Simplifying
x + 4.5 = 14.291605928

Reorder the terms:
4.5 + x = 14.291605928

Solving
4.5 + x = 14.291605928

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 14.291605928 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 14.291605928 + -4.5
x = 14.291605928 + -4.5

Combine like terms: 14.291605928 + -4.5 = 9.791605928
x = 9.791605928

Simplifying
x = 9.791605928


Subproblem 2
x + 4.5 = -14.291605928

Simplifying
x + 4.5 = -14.291605928

Reorder the terms:
4.5 + x = -14.291605928

Solving
4.5 + x = -14.291605928

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -14.291605928 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -14.291605928 + -4.5
x = -14.291605928 + -4.5

Combine like terms: -14.291605928 + -4.5 = -18.791605928
x = -18.791605928

Simplifying
x = -18.791605928


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.791605928, -18.791605928}

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