0=3x^2+12x+5

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Solution for 0=3x^2+12x+5 equation: 


Simplifying
0 = 3x2 + 12x + 5

Reorder the terms:
0 = 5 + 12x + 3x2

Solving
0 = 5 + 12x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + -5 = -5
-5 + -12x + -3x2 = 5 + 12x + 3x2 + -5 + -12x + -3x2

Reorder the terms:
-5 + -12x + -3x2 = 5 + -5 + 12x + -12x + 3x2 + -3x2

Combine like terms: 5 + -5 = 0
-5 + -12x + -3x2 = 0 + 12x + -12x + 3x2 + -3x2
-5 + -12x + -3x2 = 12x + -12x + 3x2 + -3x2

Combine like terms: 12x + -12x = 0
-5 + -12x + -3x2 = 0 + 3x2 + -3x2
-5 + -12x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-5 + -12x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 12x + 3x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(5 + 12x + 3x2)' equal to zero and attempt to solve:

Simplifying
5 + 12x + 3x2 = 0

Solving
5 + 12x + 3x2 = 0

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

Divide each side by '3'.
1.666666667 + 4x + x2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + 4x + -1.666666667 + x2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + 4x + x2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + 4x + x2 = 0 + -1.666666667
4x + x2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
4x + x2 = -1.666666667

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = -1.666666667 + 4

Reorder the terms:
4 + 4x + x2 = -1.666666667 + 4

Combine like terms: -1.666666667 + 4 = 2.333333333
4 + 4x + x2 = 2.333333333

Factor a perfect square on the left side:
(x + 2)(x + 2) = 2.333333333

Calculate the square root of the right side: 1.527525232

Break this problem into two subproblems by setting 
(x + 2) equal to 1.527525232 and -1.527525232.


Subproblem 1
x + 2 = 1.527525232

Simplifying
x + 2 = 1.527525232

Reorder the terms:
2 + x = 1.527525232

Solving
2 + x = 1.527525232

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 1.527525232 + -2

Combine like terms: 2 + -2 = 0
0 + x = 1.527525232 + -2
x = 1.527525232 + -2

Combine like terms: 1.527525232 + -2 = -0.472474768
x = -0.472474768

Simplifying
x = -0.472474768


Subproblem 2
x + 2 = -1.527525232

Simplifying
x + 2 = -1.527525232

Reorder the terms:
2 + x = -1.527525232

Solving
2 + x = -1.527525232

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -1.527525232 + -2

Combine like terms: 2 + -2 = 0
0 + x = -1.527525232 + -2
x = -1.527525232 + -2

Combine like terms: -1.527525232 + -2 = -3.527525232
x = -3.527525232

Simplifying
x = -3.527525232


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.472474768, -3.527525232}
Solution
x = {-0.472474768, -3.527525232}

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