a^2+2a-34=0

Solution for a^2+2a-34=0 equation:

Simplifying
a2 + 2a + -34 = 0

Reorder the terms:
-34 + 2a + a2 = 0

Solving
-34 + 2a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '34' to each side of the equation.
-34 + 2a + 34 + a2 = 0 + 34

Reorder the terms:
-34 + 34 + 2a + a2 = 0 + 34

Combine like terms: -34 + 34 = 0
0 + 2a + a2 = 0 + 34
2a + a2 = 0 + 34

Combine like terms: 0 + 34 = 34
2a + a2 = 34

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 = 34 + 1

Reorder the terms:
1 + 2a + a2 = 34 + 1

Combine like terms: 34 + 1 = 35
1 + 2a + a2 = 35

Factor a perfect square on the left side:
(a + 1)(a + 1) = 35

Calculate the square root of the right side: 5.916079783

Break this problem into two subproblems by setting 
(a + 1) equal to 5.916079783 and -5.916079783.

Subproblem 1
a + 1 = 5.916079783

Simplifying
a + 1 = 5.916079783

Reorder the terms:
1 + a = 5.916079783

Solving
1 + a = 5.916079783

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 = 5.916079783 + -1

Combine like terms: 1 + -1 = 0
0 + a = 5.916079783 + -1
a = 5.916079783 + -1

Combine like terms: 5.916079783 + -1 = 4.916079783
a = 4.916079783

Simplifying
a = 4.916079783

Subproblem 2
a + 1 = -5.916079783

Simplifying
a + 1 = -5.916079783

Reorder the terms:
1 + a = -5.916079783

Solving
1 + a = -5.916079783

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 = -5.916079783 + -1

Combine like terms: 1 + -1 = 0
0 + a = -5.916079783 + -1
a = -5.916079783 + -1

Combine like terms: -5.916079783 + -1 = -6.916079783
a = -6.916079783

Simplifying
a = -6.916079783

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {4.916079783, -6.916079783}