0.003x^2+35x-42=0

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Solution for 0.003x^2+35x-42=0 equation: 


Simplifying
0.003x2 + 35x + -42 = 0

Reorder the terms:
-42 + 35x + 0.003x2 = 0

Solving
-42 + 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'.
-14000 + 11666.66667x + x2 = 0

Move the constant term to the right:

Add '14000' to each side of the equation.
-14000 + 11666.66667x + 14000 + x2 = 0 + 14000

Reorder the terms:
-14000 + 14000 + 11666.66667x + x2 = 0 + 14000

Combine like terms: -14000 + 14000 = 0
0 + 11666.66667x + x2 = 0 + 14000
11666.66667x + x2 = 0 + 14000

Combine like terms: 0 + 14000 = 14000
11666.66667x + x2 = 14000

The x term is 11666.66667x.  Take half its coefficient (5833.333335).
Square it (34027777.80) and add it to both sides.

Add '34027777.80' to each side of the equation.
11666.66667x + 34027777.80 + x2 = 14000 + 34027777.80

Reorder the terms:
34027777.80 + 11666.66667x + x2 = 14000 + 34027777.80

Combine like terms: 14000 + 34027777.80 = 34041777.8
34027777.80 + 11666.66667x + x2 = 34041777.8

Factor a perfect square on the left side:
(x + 5833.333335)(x + 5833.333335) = 34041777.8

Calculate the square root of the right side: 5834.533211835

Break this problem into two subproblems by setting 
(x + 5833.333335) equal to 5834.533211835 and -5834.533211835.


Subproblem 1
x + 5833.333335 = 5834.533211835

Simplifying
x + 5833.333335 = 5834.533211835

Reorder the terms:
5833.333335 + x = 5834.533211835

Solving
5833.333335 + x = 5834.533211835

Solving for variable 'x'.

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

Add '-5833.333335' to each side of the equation.
5833.333335 + -5833.333335 + x = 5834.533211835 + -5833.333335

Combine like terms: 5833.333335 + -5833.333335 = 0.000000
0.000000 + x = 5834.533211835 + -5833.333335
x = 5834.533211835 + -5833.333335

Combine like terms: 5834.533211835 + -5833.333335 = 1.199876835
x = 1.199876835

Simplifying
x = 1.199876835


Subproblem 2
x + 5833.333335 = -5834.533211835

Simplifying
x + 5833.333335 = -5834.533211835

Reorder the terms:
5833.333335 + x = -5834.533211835

Solving
5833.333335 + x = -5834.533211835

Solving for variable 'x'.

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

Add '-5833.333335' to each side of the equation.
5833.333335 + -5833.333335 + x = -5834.533211835 + -5833.333335

Combine like terms: 5833.333335 + -5833.333335 = 0.000000
0.000000 + x = -5834.533211835 + -5833.333335
x = -5834.533211835 + -5833.333335

Combine like terms: -5834.533211835 + -5833.333335 = -11667.866546835
x = -11667.866546835

Simplifying
x = -11667.866546835


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.199876835, -11667.866546835}

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