A^2-3A-3=5

Solution for A^2-3A-3=5 equation:

Simplifying
A2 + -3A + -3 = 5

Reorder the terms:
-3 + -3A + A2 = 5

Solving
-3 + -3A + A2 = 5

Solving for variable 'A'.

Reorder the terms:
-3 + -5 + -3A + A2 = 5 + -5

Combine like terms: -3 + -5 = -8
-8 + -3A + A2 = 5 + -5

Combine like terms: 5 + -5 = 0
-8 + -3A + A2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -3A + 8 + A2 = 0 + 8

Reorder the terms:
-8 + 8 + -3A + A2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3A + A2 = 0 + 8
-3A + A2 = 0 + 8

Combine like terms: 0 + 8 = 8
-3A + A2 = 8

The A term is -3A.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3A + 2.25 + A2 = 8 + 2.25

Reorder the terms:
2.25 + -3A + A2 = 8 + 2.25

Combine like terms: 8 + 2.25 = 10.25
2.25 + -3A + A2 = 10.25

Factor a perfect square on the left side:
(A + -1.5)(A + -1.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(A + -1.5) equal to 3.201562119 and -3.201562119.

Subproblem 1
A + -1.5 = 3.201562119

Simplifying
A + -1.5 = 3.201562119

Reorder the terms:
-1.5 + A = 3.201562119

Solving
-1.5 + A = 3.201562119

Solving for variable 'A'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + A = 3.201562119 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + A = 3.201562119 + 1.5
A = 3.201562119 + 1.5

Combine like terms: 3.201562119 + 1.5 = 4.701562119
A = 4.701562119

Simplifying
A = 4.701562119

Subproblem 2
A + -1.5 = -3.201562119

Simplifying
A + -1.5 = -3.201562119

Reorder the terms:
-1.5 + A = -3.201562119

Solving
-1.5 + A = -3.201562119

Solving for variable 'A'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + A = -3.201562119 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + A = -3.201562119 + 1.5
A = -3.201562119 + 1.5

Combine like terms: -3.201562119 + 1.5 = -1.701562119
A = -1.701562119

Simplifying
A = -1.701562119

Solution
The solution to the problem is based on the solutions
from the subproblems.
A = {4.701562119, -1.701562119}