1800+3200x+160x*x=0

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Solution for 1800+3200x+160x*x=0 equation: 


Simplifying
1800 + 3200x + 160x * x = 0

Multiply x * x
1800 + 3200x + 160x2 = 0

Solving
1800 + 3200x + 160x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '40'.
40(45 + 80x + 4x2) = 0

Ignore the factor 40.

Subproblem 1
Set the factor '(45 + 80x + 4x2)' equal to zero and attempt to solve:

Simplifying
45 + 80x + 4x2 = 0

Solving
45 + 80x + 4x2 = 0

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

Divide each side by '4'.
11.25 + 20x + x2 = 0

Move the constant term to the right:

Add '-11.25' to each side of the equation.
11.25 + 20x + -11.25 + x2 = 0 + -11.25

Reorder the terms:
11.25 + -11.25 + 20x + x2 = 0 + -11.25

Combine like terms: 11.25 + -11.25 = 0.00
0.00 + 20x + x2 = 0 + -11.25
20x + x2 = 0 + -11.25

Combine like terms: 0 + -11.25 = -11.25
20x + x2 = -11.25

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = -11.25 + 100

Reorder the terms:
100 + 20x + x2 = -11.25 + 100

Combine like terms: -11.25 + 100 = 88.75
100 + 20x + x2 = 88.75

Factor a perfect square on the left side:
(x + 10)(x + 10) = 88.75

Calculate the square root of the right side: 9.420721841

Break this problem into two subproblems by setting 
(x + 10) equal to 9.420721841 and -9.420721841.


Subproblem 1
x + 10 = 9.420721841

Simplifying
x + 10 = 9.420721841

Reorder the terms:
10 + x = 9.420721841

Solving
10 + x = 9.420721841

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = 9.420721841 + -10

Combine like terms: 10 + -10 = 0
0 + x = 9.420721841 + -10
x = 9.420721841 + -10

Combine like terms: 9.420721841 + -10 = -0.579278159
x = -0.579278159

Simplifying
x = -0.579278159


Subproblem 2
x + 10 = -9.420721841

Simplifying
x + 10 = -9.420721841

Reorder the terms:
10 + x = -9.420721841

Solving
10 + x = -9.420721841

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = -9.420721841 + -10

Combine like terms: 10 + -10 = 0
0 + x = -9.420721841 + -10
x = -9.420721841 + -10

Combine like terms: -9.420721841 + -10 = -19.420721841
x = -19.420721841

Simplifying
x = -19.420721841


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.579278159, -19.420721841}
Solution
x = {-0.579278159, -19.420721841}

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