a^2+6a-18=0

Solution for a^2+6a-18=0 equation:

Simplifying
a2 + 6a + -18 = 0

Reorder the terms:
-18 + 6a + a2 = 0

Solving
-18 + 6a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + 6a + 18 + a2 = 0 + 18

Reorder the terms:
-18 + 18 + 6a + a2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 6a + a2 = 0 + 18
6a + a2 = 0 + 18

Combine like terms: 0 + 18 = 18
6a + a2 = 18

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 = 18 + 9

Reorder the terms:
9 + 6a + a2 = 18 + 9

Combine like terms: 18 + 9 = 27
9 + 6a + a2 = 27

Factor a perfect square on the left side:
(a + 3)(a + 3) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(a + 3) equal to 5.196152423 and -5.196152423.

Subproblem 1
a + 3 = 5.196152423

Simplifying
a + 3 = 5.196152423

Reorder the terms:
3 + a = 5.196152423

Solving
3 + a = 5.196152423

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 = 5.196152423 + -3

Combine like terms: 3 + -3 = 0
0 + a = 5.196152423 + -3
a = 5.196152423 + -3

Combine like terms: 5.196152423 + -3 = 2.196152423
a = 2.196152423

Simplifying
a = 2.196152423

Subproblem 2
a + 3 = -5.196152423

Simplifying
a + 3 = -5.196152423

Reorder the terms:
3 + a = -5.196152423

Solving
3 + a = -5.196152423

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 = -5.196152423 + -3

Combine like terms: 3 + -3 = 0
0 + a = -5.196152423 + -3
a = -5.196152423 + -3

Combine like terms: -5.196152423 + -3 = -8.196152423
a = -8.196152423

Simplifying
a = -8.196152423

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {2.196152423, -8.196152423}