a^2+2a-36=0

Solution for a^2+2a-36=0 equation:

Simplifying
a2 + 2a + -36 = 0

Reorder the terms:
-36 + 2a + a2 = 0

Solving
-36 + 2a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + 2a + 36 + a2 = 0 + 36

Reorder the terms:
-36 + 36 + 2a + a2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 2a + a2 = 0 + 36
2a + a2 = 0 + 36

Combine like terms: 0 + 36 = 36
2a + a2 = 36

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 = 36 + 1

Reorder the terms:
1 + 2a + a2 = 36 + 1

Combine like terms: 36 + 1 = 37
1 + 2a + a2 = 37

Factor a perfect square on the left side:
(a + 1)(a + 1) = 37

Calculate the square root of the right side: 6.08276253

Break this problem into two subproblems by setting 
(a + 1) equal to 6.08276253 and -6.08276253.

Subproblem 1
a + 1 = 6.08276253

Simplifying
a + 1 = 6.08276253

Reorder the terms:
1 + a = 6.08276253

Solving
1 + a = 6.08276253

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 = 6.08276253 + -1

Combine like terms: 1 + -1 = 0
0 + a = 6.08276253 + -1
a = 6.08276253 + -1

Combine like terms: 6.08276253 + -1 = 5.08276253
a = 5.08276253

Simplifying
a = 5.08276253

Subproblem 2
a + 1 = -6.08276253

Simplifying
a + 1 = -6.08276253

Reorder the terms:
1 + a = -6.08276253

Solving
1 + a = -6.08276253

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 = -6.08276253 + -1

Combine like terms: 1 + -1 = 0
0 + a = -6.08276253 + -1
a = -6.08276253 + -1

Combine like terms: -6.08276253 + -1 = -7.08276253
a = -7.08276253

Simplifying
a = -7.08276253

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {5.08276253, -7.08276253}