160x^2+9328x+33280=0

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Solution for 160x^2+9328x+33280=0 equation: 


Simplifying
160x2 + 9328x + 33280 = 0

Reorder the terms:
33280 + 9328x + 160x2 = 0

Solving
33280 + 9328x + 160x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '16'.
16(2080 + 583x + 10x2) = 0

Ignore the factor 16.

Subproblem 1
Set the factor '(2080 + 583x + 10x2)' equal to zero and attempt to solve:

Simplifying
2080 + 583x + 10x2 = 0

Solving
2080 + 583x + 10x2 = 0

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

Divide each side by '10'.
208 + 58.3x + x2 = 0.0

Move the constant term to the right:

Add '-208' to each side of the equation.
208 + 58.3x + -208 + x2 = 0.0 + -208

Reorder the terms:
208 + -208 + 58.3x + x2 = 0.0 + -208

Combine like terms: 208 + -208 = 0
0 + 58.3x + x2 = 0.0 + -208
58.3x + x2 = 0.0 + -208

Combine like terms: 0.0 + -208 = -208
58.3x + x2 = -208

The x term is 58.3x.  Take half its coefficient (29.15).
Square it (849.7225) and add it to both sides.

Add '849.7225' to each side of the equation.
58.3x + 849.7225 + x2 = -208 + 849.7225

Reorder the terms:
849.7225 + 58.3x + x2 = -208 + 849.7225

Combine like terms: -208 + 849.7225 = 641.7225
849.7225 + 58.3x + x2 = 641.7225

Factor a perfect square on the left side:
(x + 29.15)(x + 29.15) = 641.7225

Calculate the square root of the right side: 25.332242301

Break this problem into two subproblems by setting 
(x + 29.15) equal to 25.332242301 and -25.332242301.


Subproblem 1
x + 29.15 = 25.332242301

Simplifying
x + 29.15 = 25.332242301

Reorder the terms:
29.15 + x = 25.332242301

Solving
29.15 + x = 25.332242301

Solving for variable 'x'.

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

Add '-29.15' to each side of the equation.
29.15 + -29.15 + x = 25.332242301 + -29.15

Combine like terms: 29.15 + -29.15 = 0.00
0.00 + x = 25.332242301 + -29.15
x = 25.332242301 + -29.15

Combine like terms: 25.332242301 + -29.15 = -3.817757699
x = -3.817757699

Simplifying
x = -3.817757699


Subproblem 2
x + 29.15 = -25.332242301

Simplifying
x + 29.15 = -25.332242301

Reorder the terms:
29.15 + x = -25.332242301

Solving
29.15 + x = -25.332242301

Solving for variable 'x'.

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

Add '-29.15' to each side of the equation.
29.15 + -29.15 + x = -25.332242301 + -29.15

Combine like terms: 29.15 + -29.15 = 0.00
0.00 + x = -25.332242301 + -29.15
x = -25.332242301 + -29.15

Combine like terms: -25.332242301 + -29.15 = -54.482242301
x = -54.482242301

Simplifying
x = -54.482242301


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.817757699, -54.482242301}
Solution
x = {-3.817757699, -54.482242301}

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