0.0001x^2-0.17x-1.65=0

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Solution for 0.0001x^2-0.17x-1.65=0 equation: 


Simplifying
0.0001x2 + -0.17x + -1.65 = 0

Reorder the terms:
-1.65 + -0.17x + 0.0001x2 = 0

Solving
-1.65 + -0.17x + 0.0001x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
0.0001 the coefficient of the squared term: 

Divide each side by '0.0001'.
-16500 + -1700x + x2 = 0

Move the constant term to the right:

Add '16500' to each side of the equation.
-16500 + -1700x + 16500 + x2 = 0 + 16500

Reorder the terms:
-16500 + 16500 + -1700x + x2 = 0 + 16500

Combine like terms: -16500 + 16500 = 0
0 + -1700x + x2 = 0 + 16500
-1700x + x2 = 0 + 16500

Combine like terms: 0 + 16500 = 16500
-1700x + x2 = 16500

The x term is -1700x.  Take half its coefficient (-850).
Square it (722500) and add it to both sides.

Add '722500' to each side of the equation.
-1700x + 722500 + x2 = 16500 + 722500

Reorder the terms:
722500 + -1700x + x2 = 16500 + 722500

Combine like terms: 16500 + 722500 = 739000
722500 + -1700x + x2 = 739000

Factor a perfect square on the left side:
(x + -850)(x + -850) = 739000

Calculate the square root of the right side: 859.651092013

Break this problem into two subproblems by setting 
(x + -850) equal to 859.651092013 and -859.651092013.


Subproblem 1
x + -850 = 859.651092013

Simplifying
x + -850 = 859.651092013

Reorder the terms:
-850 + x = 859.651092013

Solving
-850 + x = 859.651092013

Solving for variable 'x'.

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

Add '850' to each side of the equation.
-850 + 850 + x = 859.651092013 + 850

Combine like terms: -850 + 850 = 0
0 + x = 859.651092013 + 850
x = 859.651092013 + 850

Combine like terms: 859.651092013 + 850 = 1709.651092013
x = 1709.651092013

Simplifying
x = 1709.651092013


Subproblem 2
x + -850 = -859.651092013

Simplifying
x + -850 = -859.651092013

Reorder the terms:
-850 + x = -859.651092013

Solving
-850 + x = -859.651092013

Solving for variable 'x'.

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

Add '850' to each side of the equation.
-850 + 850 + x = -859.651092013 + 850

Combine like terms: -850 + 850 = 0
0 + x = -859.651092013 + 850
x = -859.651092013 + 850

Combine like terms: -859.651092013 + 850 = -9.651092013
x = -9.651092013

Simplifying
x = -9.651092013


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1709.651092013, -9.651092013}

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