12x^2+60x+50=0

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Solution for 12x^2+60x+50=0 equation: 


Simplifying
12x2 + 60x + 50 = 0

Reorder the terms:
50 + 60x + 12x2 = 0

Solving
50 + 60x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(25 + 30x + 6x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(25 + 30x + 6x2)' equal to zero and attempt to solve:

Simplifying
25 + 30x + 6x2 = 0

Solving
25 + 30x + 6x2 = 0

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

Divide each side by '6'.
4.166666667 + 5x + x2 = 0

Move the constant term to the right:

Add '-4.166666667' to each side of the equation.
4.166666667 + 5x + -4.166666667 + x2 = 0 + -4.166666667

Reorder the terms:
4.166666667 + -4.166666667 + 5x + x2 = 0 + -4.166666667

Combine like terms: 4.166666667 + -4.166666667 = 0.000000000
0.000000000 + 5x + x2 = 0 + -4.166666667
5x + x2 = 0 + -4.166666667

Combine like terms: 0 + -4.166666667 = -4.166666667
5x + x2 = -4.166666667

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = -4.166666667 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -4.166666667 + 6.25

Combine like terms: -4.166666667 + 6.25 = 2.083333333
6.25 + 5x + x2 = 2.083333333

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 2.083333333

Calculate the square root of the right side: 1.443375673

Break this problem into two subproblems by setting 
(x + 2.5) equal to 1.443375673 and -1.443375673.


Subproblem 1
x + 2.5 = 1.443375673

Simplifying
x + 2.5 = 1.443375673

Reorder the terms:
2.5 + x = 1.443375673

Solving
2.5 + x = 1.443375673

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 1.443375673 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 1.443375673 + -2.5
x = 1.443375673 + -2.5

Combine like terms: 1.443375673 + -2.5 = -1.056624327
x = -1.056624327

Simplifying
x = -1.056624327


Subproblem 2
x + 2.5 = -1.443375673

Simplifying
x + 2.5 = -1.443375673

Reorder the terms:
2.5 + x = -1.443375673

Solving
2.5 + x = -1.443375673

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -1.443375673 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -1.443375673 + -2.5
x = -1.443375673 + -2.5

Combine like terms: -1.443375673 + -2.5 = -3.943375673
x = -3.943375673

Simplifying
x = -3.943375673


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.056624327, -3.943375673}
Solution
x = {-1.056624327, -3.943375673}

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