x^2+8x-34=0

Solution for x^2+8x-34=0 equation:

Simplifying
x2 + 8x + -34 = 0

Reorder the terms:
-34 + 8x + x2 = 0

Solving
-34 + 8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '34' to each side of the equation.
-34 + 8x + 34 + x2 = 0 + 34

Reorder the terms:
-34 + 34 + 8x + x2 = 0 + 34

Combine like terms: -34 + 34 = 0
0 + 8x + x2 = 0 + 34
8x + x2 = 0 + 34

Combine like terms: 0 + 34 = 34
8x + x2 = 34

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 34 + 16

Reorder the terms:
16 + 8x + x2 = 34 + 16

Combine like terms: 34 + 16 = 50
16 + 8x + x2 = 50

Factor a perfect square on the left side:
(x + 4)(x + 4) = 50

Calculate the square root of the right side: 7.071067812

Break this problem into two subproblems by setting 
(x + 4) equal to 7.071067812 and -7.071067812.

Subproblem 1
x + 4 = 7.071067812

Simplifying
x + 4 = 7.071067812

Reorder the terms:
4 + x = 7.071067812

Solving
4 + x = 7.071067812

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 7.071067812 + -4

Combine like terms: 4 + -4 = 0
0 + x = 7.071067812 + -4
x = 7.071067812 + -4

Combine like terms: 7.071067812 + -4 = 3.071067812
x = 3.071067812

Simplifying
x = 3.071067812

Subproblem 2
x + 4 = -7.071067812

Simplifying
x + 4 = -7.071067812

Reorder the terms:
4 + x = -7.071067812

Solving
4 + x = -7.071067812

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -7.071067812 + -4

Combine like terms: 4 + -4 = 0
0 + x = -7.071067812 + -4
x = -7.071067812 + -4

Combine like terms: -7.071067812 + -4 = -11.071067812
x = -11.071067812

Simplifying
x = -11.071067812

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.071067812, -11.071067812}