-0.003x^2+x+166.6666667=0

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Solution for -0.003x^2+x+166.6666667=0 equation: 


Simplifying
-0.003x2 + x + 166.6666667 = 0

Reorder the terms:
166.6666667 + x + -0.003x2 = 0

Solving
166.6666667 + x + -0.003x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.003 the coefficient of the squared term: 

Divide each side by '-0.003'.
-55555.55557 + -333.3333333x + x2 = 0

Move the constant term to the right:

Add '55555.55557' to each side of the equation.
-55555.55557 + -333.3333333x + 55555.55557 + x2 = 0 + 55555.55557

Reorder the terms:
-55555.55557 + 55555.55557 + -333.3333333x + x2 = 0 + 55555.55557

Combine like terms: -55555.55557 + 55555.55557 = 0.00000
0.00000 + -333.3333333x + x2 = 0 + 55555.55557
-333.3333333x + x2 = 0 + 55555.55557

Combine like terms: 0 + 55555.55557 = 55555.55557
-333.3333333x + x2 = 55555.55557

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-333.3333333x + 0.25 + x2 = 55555.55557 + 0.25

Reorder the terms:
0.25 + -333.3333333x + x2 = 55555.55557 + 0.25

Combine like terms: 55555.55557 + 0.25 = 55555.80557
0.25 + -333.3333333x + x2 = 55555.80557

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 55555.80557

Calculate the square root of the right side: 235.702790756

Break this problem into two subproblems by setting 
(x + 0.5) equal to 235.702790756 and -235.702790756.


Subproblem 1
x + 0.5 = 235.702790756

Simplifying
x + 0.5 = 235.702790756

Reorder the terms:
0.5 + x = 235.702790756

Solving
0.5 + x = 235.702790756

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 235.702790756 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 235.702790756 + -0.5
x = 235.702790756 + -0.5

Combine like terms: 235.702790756 + -0.5 = 235.202790756
x = 235.202790756

Simplifying
x = 235.202790756


Subproblem 2
x + 0.5 = -235.702790756

Simplifying
x + 0.5 = -235.702790756

Reorder the terms:
0.5 + x = -235.702790756

Solving
0.5 + x = -235.702790756

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -235.702790756 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -235.702790756 + -0.5
x = -235.702790756 + -0.5

Combine like terms: -235.702790756 + -0.5 = -236.202790756
x = -236.202790756

Simplifying
x = -236.202790756


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {235.202790756, -236.202790756}

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