0.006x^2+0.923x+0.361=0

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Solution for 0.006x^2+0.923x+0.361=0 equation: 


Simplifying
0.006x2 + 0.923x + 0.361 = 0

Reorder the terms:
0.361 + 0.923x + 0.006x2 = 0

Solving
0.361 + 0.923x + 0.006x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.006'.
60.16666667 + 153.8333333x + x2 = 0

Move the constant term to the right:

Add '-60.16666667' to each side of the equation.
60.16666667 + 153.8333333x + -60.16666667 + x2 = 0 + -60.16666667

Reorder the terms:
60.16666667 + -60.16666667 + 153.8333333x + x2 = 0 + -60.16666667

Combine like terms: 60.16666667 + -60.16666667 = 0.00000000
0.00000000 + 153.8333333x + x2 = 0 + -60.16666667
153.8333333x + x2 = 0 + -60.16666667

Combine like terms: 0 + -60.16666667 = -60.16666667
153.8333333x + x2 = -60.16666667

The x term is 153.8333333x.  Take half its coefficient (76.91666665).
Square it (5916.173609) and add it to both sides.

Add '5916.173609' to each side of the equation.
153.8333333x + 5916.173609 + x2 = -60.16666667 + 5916.173609

Reorder the terms:
5916.173609 + 153.8333333x + x2 = -60.16666667 + 5916.173609

Combine like terms: -60.16666667 + 5916.173609 = 5856.00694233
5916.173609 + 153.8333333x + x2 = 5856.00694233

Factor a perfect square on the left side:
(x + 76.91666665)(x + 76.91666665) = 5856.00694233

Calculate the square root of the right side: 76.524551239

Break this problem into two subproblems by setting 
(x + 76.91666665) equal to 76.524551239 and -76.524551239.


Subproblem 1
x + 76.91666665 = 76.524551239

Simplifying
x + 76.91666665 = 76.524551239

Reorder the terms:
76.91666665 + x = 76.524551239

Solving
76.91666665 + x = 76.524551239

Solving for variable 'x'.

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

Add '-76.91666665' to each side of the equation.
76.91666665 + -76.91666665 + x = 76.524551239 + -76.91666665

Combine like terms: 76.91666665 + -76.91666665 = 0.00000000
0.00000000 + x = 76.524551239 + -76.91666665
x = 76.524551239 + -76.91666665

Combine like terms: 76.524551239 + -76.91666665 = -0.392115411
x = -0.392115411

Simplifying
x = -0.392115411


Subproblem 2
x + 76.91666665 = -76.524551239

Simplifying
x + 76.91666665 = -76.524551239

Reorder the terms:
76.91666665 + x = -76.524551239

Solving
76.91666665 + x = -76.524551239

Solving for variable 'x'.

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

Add '-76.91666665' to each side of the equation.
76.91666665 + -76.91666665 + x = -76.524551239 + -76.91666665

Combine like terms: 76.91666665 + -76.91666665 = 0.00000000
0.00000000 + x = -76.524551239 + -76.91666665
x = -76.524551239 + -76.91666665

Combine like terms: -76.524551239 + -76.91666665 = -153.441217889
x = -153.441217889

Simplifying
x = -153.441217889


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.392115411, -153.441217889}

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