0.003x^2+0.35x-36=0

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Solution for 0.003x^2+0.35x-36=0 equation: 


Simplifying
0.003x2 + 0.35x + -36 = 0

Reorder the terms:
-36 + 0.35x + 0.003x2 = 0

Solving
-36 + 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'.
-12000 + 116.6666667x + x2 = 0

Move the constant term to the right:

Add '12000' to each side of the equation.
-12000 + 116.6666667x + 12000 + x2 = 0 + 12000

Reorder the terms:
-12000 + 12000 + 116.6666667x + x2 = 0 + 12000

Combine like terms: -12000 + 12000 = 0
0 + 116.6666667x + x2 = 0 + 12000
116.6666667x + x2 = 0 + 12000

Combine like terms: 0 + 12000 = 12000
116.6666667x + x2 = 12000

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 = 12000 + 3402.777780

Reorder the terms:
3402.777780 + 116.6666667x + x2 = 12000 + 3402.777780

Combine like terms: 12000 + 3402.777780 = 15402.77778
3402.777780 + 116.6666667x + x2 = 15402.77778

Factor a perfect square on the left side:
(x + 58.33333335)(x + 58.33333335) = 15402.77778

Calculate the square root of the right side: 124.10792795

Break this problem into two subproblems by setting 
(x + 58.33333335) equal to 124.10792795 and -124.10792795.


Subproblem 1
x + 58.33333335 = 124.10792795

Simplifying
x + 58.33333335 = 124.10792795

Reorder the terms:
58.33333335 + x = 124.10792795

Solving
58.33333335 + x = 124.10792795

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 = 124.10792795 + -58.33333335

Combine like terms: 58.33333335 + -58.33333335 = 0.00000000
0.00000000 + x = 124.10792795 + -58.33333335
x = 124.10792795 + -58.33333335

Combine like terms: 124.10792795 + -58.33333335 = 65.7745946
x = 65.7745946

Simplifying
x = 65.7745946


Subproblem 2
x + 58.33333335 = -124.10792795

Simplifying
x + 58.33333335 = -124.10792795

Reorder the terms:
58.33333335 + x = -124.10792795

Solving
58.33333335 + x = -124.10792795

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 = -124.10792795 + -58.33333335

Combine like terms: 58.33333335 + -58.33333335 = 0.00000000
0.00000000 + x = -124.10792795 + -58.33333335
x = -124.10792795 + -58.33333335

Combine like terms: -124.10792795 + -58.33333335 = -182.4412613
x = -182.4412613

Simplifying
x = -182.4412613


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {65.7745946, -182.4412613}

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