6a^2-28a-16=0

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Solution for 6a^2-28a-16=0 equation: 


Simplifying
6a2 + -28a + -16 = 0

Reorder the terms:
-16 + -28a + 6a2 = 0

Solving
-16 + -28a + 6a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + -14a + 3a2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-8 + -14a + 3a2)' equal to zero and attempt to solve:

Simplifying
-8 + -14a + 3a2 = 0

Solving
-8 + -14a + 3a2 = 0

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

Divide each side by '3'.
-2.666666667 + -4.666666667a + a2 = 0

Move the constant term to the right:

Add '2.666666667' to each side of the equation.
-2.666666667 + -4.666666667a + 2.666666667 + a2 = 0 + 2.666666667

Reorder the terms:
-2.666666667 + 2.666666667 + -4.666666667a + a2 = 0 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + -4.666666667a + a2 = 0 + 2.666666667
-4.666666667a + a2 = 0 + 2.666666667

Combine like terms: 0 + 2.666666667 = 2.666666667
-4.666666667a + a2 = 2.666666667

The a term is -4.666666667a.  Take half its coefficient (-2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
-4.666666667a + 5.444444448 + a2 = 2.666666667 + 5.444444448

Reorder the terms:
5.444444448 + -4.666666667a + a2 = 2.666666667 + 5.444444448

Combine like terms: 2.666666667 + 5.444444448 = 8.111111115
5.444444448 + -4.666666667a + a2 = 8.111111115

Factor a perfect square on the left side:
(a + -2.333333334)(a + -2.333333334) = 8.111111115

Calculate the square root of the right side: 2.848001249

Break this problem into two subproblems by setting 
(a + -2.333333334) equal to 2.848001249 and -2.848001249.


Subproblem 1
a + -2.333333334 = 2.848001249

Simplifying
a + -2.333333334 = 2.848001249

Reorder the terms:
-2.333333334 + a = 2.848001249

Solving
-2.333333334 + a = 2.848001249

Solving for variable 'a'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + a = 2.848001249 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + a = 2.848001249 + 2.333333334
a = 2.848001249 + 2.333333334

Combine like terms: 2.848001249 + 2.333333334 = 5.181334583
a = 5.181334583

Simplifying
a = 5.181334583


Subproblem 2
a + -2.333333334 = -2.848001249

Simplifying
a + -2.333333334 = -2.848001249

Reorder the terms:
-2.333333334 + a = -2.848001249

Solving
-2.333333334 + a = -2.848001249

Solving for variable 'a'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + a = -2.848001249 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + a = -2.848001249 + 2.333333334
a = -2.848001249 + 2.333333334

Combine like terms: -2.848001249 + 2.333333334 = -0.514667915
a = -0.514667915

Simplifying
a = -0.514667915


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {5.181334583, -0.514667915}
Solution
a = {5.181334583, -0.514667915}

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