a^2+2a-33=0

Solution for a^2+2a-33=0 equation:

Simplifying
a2 + 2a + -33 = 0

Reorder the terms:
-33 + 2a + a2 = 0

Solving
-33 + 2a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '33' to each side of the equation.
-33 + 2a + 33 + a2 = 0 + 33

Reorder the terms:
-33 + 33 + 2a + a2 = 0 + 33

Combine like terms: -33 + 33 = 0
0 + 2a + a2 = 0 + 33
2a + a2 = 0 + 33

Combine like terms: 0 + 33 = 33
2a + a2 = 33

The a term is 2a.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2a + 1 + a2 = 33 + 1

Reorder the terms:
1 + 2a + a2 = 33 + 1

Combine like terms: 33 + 1 = 34
1 + 2a + a2 = 34

Factor a perfect square on the left side:
(a + 1)(a + 1) = 34

Calculate the square root of the right side: 5.830951895

Break this problem into two subproblems by setting 
(a + 1) equal to 5.830951895 and -5.830951895.

Subproblem 1
a + 1 = 5.830951895

Simplifying
a + 1 = 5.830951895

Reorder the terms:
1 + a = 5.830951895

Solving
1 + a = 5.830951895

Solving for variable 'a'.

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

Add '-1' to each side of the equation.
1 + -1 + a = 5.830951895 + -1

Combine like terms: 1 + -1 = 0
0 + a = 5.830951895 + -1
a = 5.830951895 + -1

Combine like terms: 5.830951895 + -1 = 4.830951895
a = 4.830951895

Simplifying
a = 4.830951895

Subproblem 2
a + 1 = -5.830951895

Simplifying
a + 1 = -5.830951895

Reorder the terms:
1 + a = -5.830951895

Solving
1 + a = -5.830951895

Solving for variable 'a'.

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

Add '-1' to each side of the equation.
1 + -1 + a = -5.830951895 + -1

Combine like terms: 1 + -1 = 0
0 + a = -5.830951895 + -1
a = -5.830951895 + -1

Combine like terms: -5.830951895 + -1 = -6.830951895
a = -6.830951895

Simplifying
a = -6.830951895

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {4.830951895, -6.830951895}