a^2-4-24-6a=0

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


Simplifying
a2 + -4 + -24 + -6a = 0

Reorder the terms:
-4 + -24 + -6a + a2 = 0

Combine like terms: -4 + -24 = -28
-28 + -6a + a2 = 0

Solving
-28 + -6a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + -6a + 28 + a2 = 0 + 28

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

Combine like terms: -28 + 28 = 0
0 + -6a + a2 = 0 + 28
-6a + a2 = 0 + 28

Combine like terms: 0 + 28 = 28
-6a + a2 = 28

The a term is -6a.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6a + 9 + a2 = 28 + 9

Reorder the terms:
9 + -6a + a2 = 28 + 9

Combine like terms: 28 + 9 = 37
9 + -6a + a2 = 37

Factor a perfect square on the left side:
(a + -3)(a + -3) = 37

Calculate the square root of the right side: 6.08276253

Break this problem into two subproblems by setting 
(a + -3) equal to 6.08276253 and -6.08276253.


Subproblem 1
a + -3 = 6.08276253

Simplifying
a + -3 = 6.08276253

Reorder the terms:
-3 + a = 6.08276253

Solving
-3 + a = 6.08276253

Solving for variable 'a'.

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

Add '3' to each side of the equation.
-3 + 3 + a = 6.08276253 + 3

Combine like terms: -3 + 3 = 0
0 + a = 6.08276253 + 3
a = 6.08276253 + 3

Combine like terms: 6.08276253 + 3 = 9.08276253
a = 9.08276253

Simplifying
a = 9.08276253


Subproblem 2
a + -3 = -6.08276253

Simplifying
a + -3 = -6.08276253

Reorder the terms:
-3 + a = -6.08276253

Solving
-3 + a = -6.08276253

Solving for variable 'a'.

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

Add '3' to each side of the equation.
-3 + 3 + a = -6.08276253 + 3

Combine like terms: -3 + 3 = 0
0 + a = -6.08276253 + 3
a = -6.08276253 + 3

Combine like terms: -6.08276253 + 3 = -3.08276253
a = -3.08276253

Simplifying
a = -3.08276253


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {9.08276253, -3.08276253}

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