a^2+2a-32=0

Solution for a^2+2a-32=0 equation:

Simplifying
a2 + 2a + -32 = 0

Reorder the terms:
-32 + 2a + a2 = 0

Solving
-32 + 2a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + 2a + 32 + a2 = 0 + 32

Reorder the terms:
-32 + 32 + 2a + a2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + 2a + a2 = 0 + 32
2a + a2 = 0 + 32

Combine like terms: 0 + 32 = 32
2a + a2 = 32

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 = 32 + 1

Reorder the terms:
1 + 2a + a2 = 32 + 1

Combine like terms: 32 + 1 = 33
1 + 2a + a2 = 33

Factor a perfect square on the left side:
(a + 1)(a + 1) = 33

Calculate the square root of the right side: 5.744562647

Break this problem into two subproblems by setting 
(a + 1) equal to 5.744562647 and -5.744562647.

Subproblem 1
a + 1 = 5.744562647

Simplifying
a + 1 = 5.744562647

Reorder the terms:
1 + a = 5.744562647

Solving
1 + a = 5.744562647

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 = 5.744562647 + -1

Combine like terms: 1 + -1 = 0
0 + a = 5.744562647 + -1
a = 5.744562647 + -1

Combine like terms: 5.744562647 + -1 = 4.744562647
a = 4.744562647

Simplifying
a = 4.744562647

Subproblem 2
a + 1 = -5.744562647

Simplifying
a + 1 = -5.744562647

Reorder the terms:
1 + a = -5.744562647

Solving
1 + a = -5.744562647

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 = -5.744562647 + -1

Combine like terms: 1 + -1 = 0
0 + a = -5.744562647 + -1
a = -5.744562647 + -1

Combine like terms: -5.744562647 + -1 = -6.744562647
a = -6.744562647

Simplifying
a = -6.744562647

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {4.744562647, -6.744562647}