5x^2+410x+300=0

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Solution for 5x^2+410x+300=0 equation: 


Simplifying
5x2 + 410x + 300 = 0

Reorder the terms:
300 + 410x + 5x2 = 0

Solving
300 + 410x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(60 + 82x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(60 + 82x + x2)' equal to zero and attempt to solve:

Simplifying
60 + 82x + x2 = 0

Solving
60 + 82x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-60' to each side of the equation.
60 + 82x + -60 + x2 = 0 + -60

Reorder the terms:
60 + -60 + 82x + x2 = 0 + -60

Combine like terms: 60 + -60 = 0
0 + 82x + x2 = 0 + -60
82x + x2 = 0 + -60

Combine like terms: 0 + -60 = -60
82x + x2 = -60

The x term is 82x.  Take half its coefficient (41).
Square it (1681) and add it to both sides.

Add '1681' to each side of the equation.
82x + 1681 + x2 = -60 + 1681

Reorder the terms:
1681 + 82x + x2 = -60 + 1681

Combine like terms: -60 + 1681 = 1621
1681 + 82x + x2 = 1621

Factor a perfect square on the left side:
(x + 41)(x + 41) = 1621

Calculate the square root of the right side: 40.261644278

Break this problem into two subproblems by setting 
(x + 41) equal to 40.261644278 and -40.261644278.


Subproblem 1
x + 41 = 40.261644278

Simplifying
x + 41 = 40.261644278

Reorder the terms:
41 + x = 40.261644278

Solving
41 + x = 40.261644278

Solving for variable 'x'.

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

Add '-41' to each side of the equation.
41 + -41 + x = 40.261644278 + -41

Combine like terms: 41 + -41 = 0
0 + x = 40.261644278 + -41
x = 40.261644278 + -41

Combine like terms: 40.261644278 + -41 = -0.738355722
x = -0.738355722

Simplifying
x = -0.738355722


Subproblem 2
x + 41 = -40.261644278

Simplifying
x + 41 = -40.261644278

Reorder the terms:
41 + x = -40.261644278

Solving
41 + x = -40.261644278

Solving for variable 'x'.

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

Add '-41' to each side of the equation.
41 + -41 + x = -40.261644278 + -41

Combine like terms: 41 + -41 = 0
0 + x = -40.261644278 + -41
x = -40.261644278 + -41

Combine like terms: -40.261644278 + -41 = -81.261644278
x = -81.261644278

Simplifying
x = -81.261644278


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.738355722, -81.261644278}
Solution
x = {-0.738355722, -81.261644278}

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