x(2x)+180x-8952064=0

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Solution for x(2x)+180x-8952064=0 equation: 


Simplifying
x(2x) + 180x + -8952064 = 0

Remove parenthesis around (2x)
x * 2x + 180x + -8952064 = 0

Reorder the terms for easier multiplication:
2x * x + 180x + -8952064 = 0

Multiply x * x
2x2 + 180x + -8952064 = 0

Reorder the terms:
-8952064 + 180x + 2x2 = 0

Solving
-8952064 + 180x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4476032 + 90x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-4476032 + 90x + x2)' equal to zero and attempt to solve:

Simplifying
-4476032 + 90x + x2 = 0

Solving
-4476032 + 90x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4476032' to each side of the equation.
-4476032 + 90x + 4476032 + x2 = 0 + 4476032

Reorder the terms:
-4476032 + 4476032 + 90x + x2 = 0 + 4476032

Combine like terms: -4476032 + 4476032 = 0
0 + 90x + x2 = 0 + 4476032
90x + x2 = 0 + 4476032

Combine like terms: 0 + 4476032 = 4476032
90x + x2 = 4476032

The x term is 90x.  Take half its coefficient (45).
Square it (2025) and add it to both sides.

Add '2025' to each side of the equation.
90x + 2025 + x2 = 4476032 + 2025

Reorder the terms:
2025 + 90x + x2 = 4476032 + 2025

Combine like terms: 4476032 + 2025 = 4478057
2025 + 90x + x2 = 4478057

Factor a perfect square on the left side:
(x + 45)(x + 45) = 4478057

Calculate the square root of the right side: 2116.142008467

Break this problem into two subproblems by setting 
(x + 45) equal to 2116.142008467 and -2116.142008467.


Subproblem 1
x + 45 = 2116.142008467

Simplifying
x + 45 = 2116.142008467

Reorder the terms:
45 + x = 2116.142008467

Solving
45 + x = 2116.142008467

Solving for variable 'x'.

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

Add '-45' to each side of the equation.
45 + -45 + x = 2116.142008467 + -45

Combine like terms: 45 + -45 = 0
0 + x = 2116.142008467 + -45
x = 2116.142008467 + -45

Combine like terms: 2116.142008467 + -45 = 2071.142008467
x = 2071.142008467

Simplifying
x = 2071.142008467


Subproblem 2
x + 45 = -2116.142008467

Simplifying
x + 45 = -2116.142008467

Reorder the terms:
45 + x = -2116.142008467

Solving
45 + x = -2116.142008467

Solving for variable 'x'.

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

Add '-45' to each side of the equation.
45 + -45 + x = -2116.142008467 + -45

Combine like terms: 45 + -45 = 0
0 + x = -2116.142008467 + -45
x = -2116.142008467 + -45

Combine like terms: -2116.142008467 + -45 = -2161.142008467
x = -2161.142008467

Simplifying
x = -2161.142008467


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2071.142008467, -2161.142008467}
Solution
x = {2071.142008467, -2161.142008467}

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