-6x^2+24x+4=0

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Solution for -6x^2+24x+4=0 equation: 


Simplifying
-6x2 + 24x + 4 = 0

Reorder the terms:
4 + 24x + -6x2 = 0

Solving
4 + 24x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + 12x + -3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(2 + 12x + -3x2)' equal to zero and attempt to solve:

Simplifying
2 + 12x + -3x2 = 0

Solving
2 + 12x + -3x2 = 0

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

Divide each side by '-3'.
-0.6666666667 + -4x + x2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + -4x + 0.6666666667 + x2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + -4x + x2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + -4x + x2 = 0 + 0.6666666667
-4x + x2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
-4x + x2 = 0.6666666667

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 = 0.6666666667 + 4

Reorder the terms:
4 + -4x + x2 = 0.6666666667 + 4

Combine like terms: 0.6666666667 + 4 = 4.6666666667
4 + -4x + x2 = 4.6666666667

Factor a perfect square on the left side:
(x + -2)(x + -2) = 4.6666666667

Calculate the square root of the right side: 2.160246899

Break this problem into two subproblems by setting 
(x + -2) equal to 2.160246899 and -2.160246899.


Subproblem 1
x + -2 = 2.160246899

Simplifying
x + -2 = 2.160246899

Reorder the terms:
-2 + x = 2.160246899

Solving
-2 + x = 2.160246899

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 = 2.160246899 + 2

Combine like terms: -2 + 2 = 0
0 + x = 2.160246899 + 2
x = 2.160246899 + 2

Combine like terms: 2.160246899 + 2 = 4.160246899
x = 4.160246899

Simplifying
x = 4.160246899


Subproblem 2
x + -2 = -2.160246899

Simplifying
x + -2 = -2.160246899

Reorder the terms:
-2 + x = -2.160246899

Solving
-2 + x = -2.160246899

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 = -2.160246899 + 2

Combine like terms: -2 + 2 = 0
0 + x = -2.160246899 + 2
x = -2.160246899 + 2

Combine like terms: -2.160246899 + 2 = -0.160246899
x = -0.160246899

Simplifying
x = -0.160246899


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.160246899, -0.160246899}
Solution
x = {4.160246899, -0.160246899}

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