3x^2+60x+60=0

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Solution for 3x^2+60x+60=0 equation:


Simplifying
3x2 + 60x + 60 = 0

Reorder the terms:
60 + 60x + 3x2 = 0

Solving
60 + 60x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(20 + 20x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(20 + 20x + x2)' equal to zero and attempt to solve:

Simplifying
20 + 20x + x2 = 0

Solving
20 + 20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = -20 + 100

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

Combine like terms: -20 + 100 = 80
100 + 20x + x2 = 80

Factor a perfect square on the left side:
(x + 10)(x + 10) = 80

Calculate the square root of the right side: 8.94427191

Break this problem into two subproblems by setting 
(x + 10) equal to 8.94427191 and -8.94427191.


Subproblem 1
x + 10 = 8.94427191

Simplifying
x + 10 = 8.94427191

Reorder the terms:
10 + x = 8.94427191

Solving
10 + x = 8.94427191

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 = 8.94427191 + -10

Combine like terms: 10 + -10 = 0
0 + x = 8.94427191 + -10
x = 8.94427191 + -10

Combine like terms: 8.94427191 + -10 = -1.05572809
x = -1.05572809

Simplifying
x = -1.05572809


Subproblem 2
x + 10 = -8.94427191

Simplifying
x + 10 = -8.94427191

Reorder the terms:
10 + x = -8.94427191

Solving
10 + x = -8.94427191

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 = -8.94427191 + -10

Combine like terms: 10 + -10 = 0
0 + x = -8.94427191 + -10
x = -8.94427191 + -10

Combine like terms: -8.94427191 + -10 = -18.94427191
x = -18.94427191

Simplifying
x = -18.94427191


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.05572809, -18.94427191}
Solution
x = {-1.05572809, -18.94427191}

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