5.5-.0018x^2-.06x=0

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Solution for 5.5-.0018x^2-.06x=0 equation: 


Simplifying
5.5 + -0.0018x2 + -0.06x = 0

Reorder the terms:
5.5 + -0.06x + -0.0018x2 = 0

Solving
5.5 + -0.06x + -0.0018x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.0018 the coefficient of the squared term: 

Divide each side by '-0.0018'.
-3055.555556 + 33.33333333x + x2 = 0

Move the constant term to the right:

Add '3055.555556' to each side of the equation.
-3055.555556 + 33.33333333x + 3055.555556 + x2 = 0 + 3055.555556

Reorder the terms:
-3055.555556 + 3055.555556 + 33.33333333x + x2 = 0 + 3055.555556

Combine like terms: -3055.555556 + 3055.555556 = 0.000000
0.000000 + 33.33333333x + x2 = 0 + 3055.555556
33.33333333x + x2 = 0 + 3055.555556

Combine like terms: 0 + 3055.555556 = 3055.555556
33.33333333x + x2 = 3055.555556

The x term is 33.33333333x.  Take half its coefficient (16.66666667).
Square it (277.7777779) and add it to both sides.

Add '277.7777779' to each side of the equation.
33.33333333x + 277.7777779 + x2 = 3055.555556 + 277.7777779

Reorder the terms:
277.7777779 + 33.33333333x + x2 = 3055.555556 + 277.7777779

Combine like terms: 3055.555556 + 277.7777779 = 3333.3333339
277.7777779 + 33.33333333x + x2 = 3333.3333339

Factor a perfect square on the left side:
(x + 16.66666667)(x + 16.66666667) = 3333.3333339

Calculate the square root of the right side: 57.735026924

Break this problem into two subproblems by setting 
(x + 16.66666667) equal to 57.735026924 and -57.735026924.


Subproblem 1
x + 16.66666667 = 57.735026924

Simplifying
x + 16.66666667 = 57.735026924

Reorder the terms:
16.66666667 + x = 57.735026924

Solving
16.66666667 + x = 57.735026924

Solving for variable 'x'.

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

Add '-16.66666667' to each side of the equation.
16.66666667 + -16.66666667 + x = 57.735026924 + -16.66666667

Combine like terms: 16.66666667 + -16.66666667 = 0.00000000
0.00000000 + x = 57.735026924 + -16.66666667
x = 57.735026924 + -16.66666667

Combine like terms: 57.735026924 + -16.66666667 = 41.068360254
x = 41.068360254

Simplifying
x = 41.068360254


Subproblem 2
x + 16.66666667 = -57.735026924

Simplifying
x + 16.66666667 = -57.735026924

Reorder the terms:
16.66666667 + x = -57.735026924

Solving
16.66666667 + x = -57.735026924

Solving for variable 'x'.

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

Add '-16.66666667' to each side of the equation.
16.66666667 + -16.66666667 + x = -57.735026924 + -16.66666667

Combine like terms: 16.66666667 + -16.66666667 = 0.00000000
0.00000000 + x = -57.735026924 + -16.66666667
x = -57.735026924 + -16.66666667

Combine like terms: -57.735026924 + -16.66666667 = -74.401693594
x = -74.401693594

Simplifying
x = -74.401693594


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {41.068360254, -74.401693594}

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