x^2+5x=184.2

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Solution for x^2+5x=184.2 equation: 


Simplifying
x2 + 5x = 184.2

Reorder the terms:
5x + x2 = 184.2

Solving
5x + x2 = 184.2

Solving for variable 'x'.

Reorder the terms:
-184.2 + 5x + x2 = 184.2 + -184.2

Combine like terms: 184.2 + -184.2 = 0.0
-184.2 + 5x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '184.2' to each side of the equation.
-184.2 + 5x + 184.2 + x2 = 0.0 + 184.2

Reorder the terms:
-184.2 + 184.2 + 5x + x2 = 0.0 + 184.2

Combine like terms: -184.2 + 184.2 = 0.0
0.0 + 5x + x2 = 0.0 + 184.2
5x + x2 = 0.0 + 184.2

Combine like terms: 0.0 + 184.2 = 184.2
5x + x2 = 184.2

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 184.2 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 184.2 + 6.25

Combine like terms: 184.2 + 6.25 = 190.45
6.25 + 5x + x2 = 190.45

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 190.45

Calculate the square root of the right side: 13.800362314

Break this problem into two subproblems by setting 
(x + 2.5) equal to 13.800362314 and -13.800362314.


Subproblem 1
x + 2.5 = 13.800362314

Simplifying
x + 2.5 = 13.800362314

Reorder the terms:
2.5 + x = 13.800362314

Solving
2.5 + x = 13.800362314

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 13.800362314 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 13.800362314 + -2.5
x = 13.800362314 + -2.5

Combine like terms: 13.800362314 + -2.5 = 11.300362314
x = 11.300362314

Simplifying
x = 11.300362314


Subproblem 2
x + 2.5 = -13.800362314

Simplifying
x + 2.5 = -13.800362314

Reorder the terms:
2.5 + x = -13.800362314

Solving
2.5 + x = -13.800362314

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -13.800362314 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -13.800362314 + -2.5
x = -13.800362314 + -2.5

Combine like terms: -13.800362314 + -2.5 = -16.300362314
x = -16.300362314

Simplifying
x = -16.300362314


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.300362314, -16.300362314}

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