x^2+8x-55=0

Solution for x^2+8x-55=0 equation:

Simplifying
x2 + 8x + -55 = 0

Reorder the terms:
-55 + 8x + x2 = 0

Solving
-55 + 8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '55' to each side of the equation.
-55 + 8x + 55 + x2 = 0 + 55

Reorder the terms:
-55 + 55 + 8x + x2 = 0 + 55

Combine like terms: -55 + 55 = 0
0 + 8x + x2 = 0 + 55
8x + x2 = 0 + 55

Combine like terms: 0 + 55 = 55
8x + x2 = 55

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 = 55 + 16

Reorder the terms:
16 + 8x + x2 = 55 + 16

Combine like terms: 55 + 16 = 71
16 + 8x + x2 = 71

Factor a perfect square on the left side:
(x + 4)(x + 4) = 71

Calculate the square root of the right side: 8.426149773

Break this problem into two subproblems by setting 
(x + 4) equal to 8.426149773 and -8.426149773.

Subproblem 1
x + 4 = 8.426149773

Simplifying
x + 4 = 8.426149773

Reorder the terms:
4 + x = 8.426149773

Solving
4 + x = 8.426149773

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 = 8.426149773 + -4

Combine like terms: 4 + -4 = 0
0 + x = 8.426149773 + -4
x = 8.426149773 + -4

Combine like terms: 8.426149773 + -4 = 4.426149773
x = 4.426149773

Simplifying
x = 4.426149773

Subproblem 2
x + 4 = -8.426149773

Simplifying
x + 4 = -8.426149773

Reorder the terms:
4 + x = -8.426149773

Solving
4 + x = -8.426149773

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 = -8.426149773 + -4

Combine like terms: 4 + -4 = 0
0 + x = -8.426149773 + -4
x = -8.426149773 + -4

Combine like terms: -8.426149773 + -4 = -12.426149773
x = -12.426149773

Simplifying
x = -12.426149773

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.426149773, -12.426149773}