6x^2+30x+8=0

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Solution for 6x^2+30x+8=0 equation: 


Simplifying
6x2 + 30x + 8 = 0

Reorder the terms:
8 + 30x + 6x2 = 0

Solving
8 + 30x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 15x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(4 + 15x + 3x2)' equal to zero and attempt to solve:

Simplifying
4 + 15x + 3x2 = 0

Solving
4 + 15x + 3x2 = 0

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

Divide each side by '3'.
1.333333333 + 5x + x2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + 5x + -1.333333333 + x2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + 5x + x2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + 5x + x2 = 0 + -1.333333333
5x + x2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
5x + x2 = -1.333333333

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 = -1.333333333 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -1.333333333 + 6.25

Combine like terms: -1.333333333 + 6.25 = 4.916666667
6.25 + 5x + x2 = 4.916666667

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 4.916666667

Calculate the square root of the right side: 2.217355783

Break this problem into two subproblems by setting 
(x + 2.5) equal to 2.217355783 and -2.217355783.


Subproblem 1
x + 2.5 = 2.217355783

Simplifying
x + 2.5 = 2.217355783

Reorder the terms:
2.5 + x = 2.217355783

Solving
2.5 + x = 2.217355783

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 = 2.217355783 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 2.217355783 + -2.5
x = 2.217355783 + -2.5

Combine like terms: 2.217355783 + -2.5 = -0.282644217
x = -0.282644217

Simplifying
x = -0.282644217


Subproblem 2
x + 2.5 = -2.217355783

Simplifying
x + 2.5 = -2.217355783

Reorder the terms:
2.5 + x = -2.217355783

Solving
2.5 + x = -2.217355783

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 = -2.217355783 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -2.217355783 + -2.5
x = -2.217355783 + -2.5

Combine like terms: -2.217355783 + -2.5 = -4.717355783
x = -4.717355783

Simplifying
x = -4.717355783


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.282644217, -4.717355783}
Solution
x = {-0.282644217, -4.717355783}

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