a^2-6a-8=0

Solution for a^2-6a-8=0 equation:

Simplifying
a2 + -6a + -8 = 0

Reorder the terms:
-8 + -6a + a2 = 0

Solving
-8 + -6a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -6a + 8 + a2 = 0 + 8

Reorder the terms:
-8 + 8 + -6a + a2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -6a + a2 = 0 + 8
-6a + a2 = 0 + 8

Combine like terms: 0 + 8 = 8
-6a + a2 = 8

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 = 8 + 9

Reorder the terms:
9 + -6a + a2 = 8 + 9

Combine like terms: 8 + 9 = 17
9 + -6a + a2 = 17

Factor a perfect square on the left side:
(a + -3)(a + -3) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(a + -3) equal to 4.123105626 and -4.123105626.

Subproblem 1
a + -3 = 4.123105626

Simplifying
a + -3 = 4.123105626

Reorder the terms:
-3 + a = 4.123105626

Solving
-3 + a = 4.123105626

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 = 4.123105626 + 3

Combine like terms: -3 + 3 = 0
0 + a = 4.123105626 + 3
a = 4.123105626 + 3

Combine like terms: 4.123105626 + 3 = 7.123105626
a = 7.123105626

Simplifying
a = 7.123105626

Subproblem 2
a + -3 = -4.123105626

Simplifying
a + -3 = -4.123105626

Reorder the terms:
-3 + a = -4.123105626

Solving
-3 + a = -4.123105626

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 = -4.123105626 + 3

Combine like terms: -3 + 3 = 0
0 + a = -4.123105626 + 3
a = -4.123105626 + 3

Combine like terms: -4.123105626 + 3 = -1.123105626
a = -1.123105626

Simplifying
a = -1.123105626

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {7.123105626, -1.123105626}