3x^2-105x-200=0

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Solution for 3x^2-105x-200=0 equation: 


Simplifying
3x2 + -105x + -200 = 0

Reorder the terms:
-200 + -105x + 3x2 = 0

Solving
-200 + -105x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-66.66666667 + -35x + x2 = 0

Move the constant term to the right:

Add '66.66666667' to each side of the equation.
-66.66666667 + -35x + 66.66666667 + x2 = 0 + 66.66666667

Reorder the terms:
-66.66666667 + 66.66666667 + -35x + x2 = 0 + 66.66666667

Combine like terms: -66.66666667 + 66.66666667 = 0.00000000
0.00000000 + -35x + x2 = 0 + 66.66666667
-35x + x2 = 0 + 66.66666667

Combine like terms: 0 + 66.66666667 = 66.66666667
-35x + x2 = 66.66666667

The x term is -35x.  Take half its coefficient (-17.5).
Square it (306.25) and add it to both sides.

Add '306.25' to each side of the equation.
-35x + 306.25 + x2 = 66.66666667 + 306.25

Reorder the terms:
306.25 + -35x + x2 = 66.66666667 + 306.25

Combine like terms: 66.66666667 + 306.25 = 372.91666667
306.25 + -35x + x2 = 372.91666667

Factor a perfect square on the left side:
(x + -17.5)(x + -17.5) = 372.91666667

Calculate the square root of the right side: 19.311050377

Break this problem into two subproblems by setting 
(x + -17.5) equal to 19.311050377 and -19.311050377.


Subproblem 1
x + -17.5 = 19.311050377

Simplifying
x + -17.5 = 19.311050377

Reorder the terms:
-17.5 + x = 19.311050377

Solving
-17.5 + x = 19.311050377

Solving for variable 'x'.

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

Add '17.5' to each side of the equation.
-17.5 + 17.5 + x = 19.311050377 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x = 19.311050377 + 17.5
x = 19.311050377 + 17.5

Combine like terms: 19.311050377 + 17.5 = 36.811050377
x = 36.811050377

Simplifying
x = 36.811050377


Subproblem 2
x + -17.5 = -19.311050377

Simplifying
x + -17.5 = -19.311050377

Reorder the terms:
-17.5 + x = -19.311050377

Solving
-17.5 + x = -19.311050377

Solving for variable 'x'.

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

Add '17.5' to each side of the equation.
-17.5 + 17.5 + x = -19.311050377 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x = -19.311050377 + 17.5
x = -19.311050377 + 17.5

Combine like terms: -19.311050377 + 17.5 = -1.811050377
x = -1.811050377

Simplifying
x = -1.811050377


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {36.811050377, -1.811050377}

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