-2x*x+1700*x+6=0

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Solution for -2x*x+1700*x+6=0 equation: 


Simplifying
-2x * x + 1700x + 6 = 0

Multiply x * x
-2x2 + 1700x + 6 = 0

Reorder the terms:
6 + 1700x + -2x2 = 0

Solving
6 + 1700x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 850x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(3 + 850x + -1x2)' equal to zero and attempt to solve:

Simplifying
3 + 850x + -1x2 = 0

Solving
3 + 850x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-3 + -850x + x2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -850x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + -850x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -850x + x2 = 0 + 3
-850x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-850x + x2 = 3

The x term is -850x.  Take half its coefficient (-425).
Square it (180625) and add it to both sides.

Add '180625' to each side of the equation.
-850x + 180625 + x2 = 3 + 180625

Reorder the terms:
180625 + -850x + x2 = 3 + 180625

Combine like terms: 3 + 180625 = 180628
180625 + -850x + x2 = 180628

Factor a perfect square on the left side:
(x + -425)(x + -425) = 180628

Calculate the square root of the right side: 425.003529397

Break this problem into two subproblems by setting 
(x + -425) equal to 425.003529397 and -425.003529397.


Subproblem 1
x + -425 = 425.003529397

Simplifying
x + -425 = 425.003529397

Reorder the terms:
-425 + x = 425.003529397

Solving
-425 + x = 425.003529397

Solving for variable 'x'.

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

Add '425' to each side of the equation.
-425 + 425 + x = 425.003529397 + 425

Combine like terms: -425 + 425 = 0
0 + x = 425.003529397 + 425
x = 425.003529397 + 425

Combine like terms: 425.003529397 + 425 = 850.003529397
x = 850.003529397

Simplifying
x = 850.003529397


Subproblem 2
x + -425 = -425.003529397

Simplifying
x + -425 = -425.003529397

Reorder the terms:
-425 + x = -425.003529397

Solving
-425 + x = -425.003529397

Solving for variable 'x'.

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

Add '425' to each side of the equation.
-425 + 425 + x = -425.003529397 + 425

Combine like terms: -425 + 425 = 0
0 + x = -425.003529397 + 425
x = -425.003529397 + 425

Combine like terms: -425.003529397 + 425 = -0.003529397
x = -0.003529397

Simplifying
x = -0.003529397


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {850.003529397, -0.003529397}
Solution
x = {850.003529397, -0.003529397}

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