6x^2+48x+16=0

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Solution for 6x^2+48x+16=0 equation: 


Simplifying
6x2 + 48x + 16 = 0

Reorder the terms:
16 + 48x + 6x2 = 0

Solving
16 + 48x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + 24x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(8 + 24x + 3x2)' equal to zero and attempt to solve:

Simplifying
8 + 24x + 3x2 = 0

Solving
8 + 24x + 3x2 = 0

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

Divide each side by '3'.
2.666666667 + 8x + x2 = 0

Move the constant term to the right:

Add '-2.666666667' to each side of the equation.
2.666666667 + 8x + -2.666666667 + x2 = 0 + -2.666666667

Reorder the terms:
2.666666667 + -2.666666667 + 8x + x2 = 0 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + 8x + x2 = 0 + -2.666666667
8x + x2 = 0 + -2.666666667

Combine like terms: 0 + -2.666666667 = -2.666666667
8x + x2 = -2.666666667

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = -2.666666667 + 16

Reorder the terms:
16 + 8x + x2 = -2.666666667 + 16

Combine like terms: -2.666666667 + 16 = 13.333333333
16 + 8x + x2 = 13.333333333

Factor a perfect square on the left side:
(x + 4)(x + 4) = 13.333333333

Calculate the square root of the right side: 3.651483717

Break this problem into two subproblems by setting 
(x + 4) equal to 3.651483717 and -3.651483717.


Subproblem 1
x + 4 = 3.651483717

Simplifying
x + 4 = 3.651483717

Reorder the terms:
4 + x = 3.651483717

Solving
4 + x = 3.651483717

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 3.651483717 + -4

Combine like terms: 4 + -4 = 0
0 + x = 3.651483717 + -4
x = 3.651483717 + -4

Combine like terms: 3.651483717 + -4 = -0.348516283
x = -0.348516283

Simplifying
x = -0.348516283


Subproblem 2
x + 4 = -3.651483717

Simplifying
x + 4 = -3.651483717

Reorder the terms:
4 + x = -3.651483717

Solving
4 + x = -3.651483717

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -3.651483717 + -4

Combine like terms: 4 + -4 = 0
0 + x = -3.651483717 + -4
x = -3.651483717 + -4

Combine like terms: -3.651483717 + -4 = -7.651483717
x = -7.651483717

Simplifying
x = -7.651483717


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.348516283, -7.651483717}
Solution
x = {-0.348516283, -7.651483717}

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