0.003x^2+0.35x-44=0

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Solution for 0.003x^2+0.35x-44=0 equation: 


Simplifying
0.003x2 + 0.35x + -44 = 0

Reorder the terms:
-44 + 0.35x + 0.003x2 = 0

Solving
-44 + 0.35x + 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'.
-14666.66667 + 116.6666667x + x2 = 0

Move the constant term to the right:

Add '14666.66667' to each side of the equation.
-14666.66667 + 116.6666667x + 14666.66667 + x2 = 0 + 14666.66667

Reorder the terms:
-14666.66667 + 14666.66667 + 116.6666667x + x2 = 0 + 14666.66667

Combine like terms: -14666.66667 + 14666.66667 = 0.00000
0.00000 + 116.6666667x + x2 = 0 + 14666.66667
116.6666667x + x2 = 0 + 14666.66667

Combine like terms: 0 + 14666.66667 = 14666.66667
116.6666667x + x2 = 14666.66667

The x term is 116.6666667x.  Take half its coefficient (58.33333335).
Square it (3402.777780) and add it to both sides.

Add '3402.777780' to each side of the equation.
116.6666667x + 3402.777780 + x2 = 14666.66667 + 3402.777780

Reorder the terms:
3402.777780 + 116.6666667x + x2 = 14666.66667 + 3402.777780

Combine like terms: 14666.66667 + 3402.777780 = 18069.44445
3402.777780 + 116.6666667x + x2 = 18069.44445

Factor a perfect square on the left side:
(x + 58.33333335)(x + 58.33333335) = 18069.44445

Calculate the square root of the right side: 134.422633697

Break this problem into two subproblems by setting 
(x + 58.33333335) equal to 134.422633697 and -134.422633697.


Subproblem 1
x + 58.33333335 = 134.422633697

Simplifying
x + 58.33333335 = 134.422633697

Reorder the terms:
58.33333335 + x = 134.422633697

Solving
58.33333335 + x = 134.422633697

Solving for variable 'x'.

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

Add '-58.33333335' to each side of the equation.
58.33333335 + -58.33333335 + x = 134.422633697 + -58.33333335

Combine like terms: 58.33333335 + -58.33333335 = 0.00000000
0.00000000 + x = 134.422633697 + -58.33333335
x = 134.422633697 + -58.33333335

Combine like terms: 134.422633697 + -58.33333335 = 76.089300347
x = 76.089300347

Simplifying
x = 76.089300347


Subproblem 2
x + 58.33333335 = -134.422633697

Simplifying
x + 58.33333335 = -134.422633697

Reorder the terms:
58.33333335 + x = -134.422633697

Solving
58.33333335 + x = -134.422633697

Solving for variable 'x'.

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

Add '-58.33333335' to each side of the equation.
58.33333335 + -58.33333335 + x = -134.422633697 + -58.33333335

Combine like terms: 58.33333335 + -58.33333335 = 0.00000000
0.00000000 + x = -134.422633697 + -58.33333335
x = -134.422633697 + -58.33333335

Combine like terms: -134.422633697 + -58.33333335 = -192.755967047
x = -192.755967047

Simplifying
x = -192.755967047


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {76.089300347, -192.755967047}

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