a^2+8a-1=0

Solution for a^2+8a-1=0 equation:

Simplifying
a2 + 8a + -1 = 0

Reorder the terms:
-1 + 8a + a2 = 0

Solving
-1 + 8a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 8a + 1 + a2 = 0 + 1

Reorder the terms:
-1 + 1 + 8a + a2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 8a + a2 = 0 + 1
8a + a2 = 0 + 1

Combine like terms: 0 + 1 = 1
8a + a2 = 1

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

Add '16' to each side of the equation.
8a + 16 + a2 = 1 + 16

Reorder the terms:
16 + 8a + a2 = 1 + 16

Combine like terms: 1 + 16 = 17
16 + 8a + a2 = 17

Factor a perfect square on the left side:
(a + 4)(a + 4) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(a + 4) equal to 4.123105626 and -4.123105626.

Subproblem 1
a + 4 = 4.123105626

Simplifying
a + 4 = 4.123105626

Reorder the terms:
4 + a = 4.123105626

Solving
4 + a = 4.123105626

Solving for variable 'a'.

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

Add '-4' to each side of the equation.
4 + -4 + a = 4.123105626 + -4

Combine like terms: 4 + -4 = 0
0 + a = 4.123105626 + -4
a = 4.123105626 + -4

Combine like terms: 4.123105626 + -4 = 0.123105626
a = 0.123105626

Simplifying
a = 0.123105626

Subproblem 2
a + 4 = -4.123105626

Simplifying
a + 4 = -4.123105626

Reorder the terms:
4 + a = -4.123105626

Solving
4 + a = -4.123105626

Solving for variable 'a'.

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

Add '-4' to each side of the equation.
4 + -4 + a = -4.123105626 + -4

Combine like terms: 4 + -4 = 0
0 + a = -4.123105626 + -4
a = -4.123105626 + -4

Combine like terms: -4.123105626 + -4 = -8.123105626
a = -8.123105626

Simplifying
a = -8.123105626

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.123105626, -8.123105626}