x^2+6-55x=2

Solution for x^2+6-55x=2 equation:

Simplifying
x2 + 6 + -55x = 2

Reorder the terms:
6 + -55x + x2 = 2

Solving
6 + -55x + x2 = 2

Solving for variable 'x'.

Reorder the terms:
6 + -2 + -55x + x2 = 2 + -2

Combine like terms: 6 + -2 = 4
4 + -55x + x2 = 2 + -2

Combine like terms: 2 + -2 = 0
4 + -55x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -55x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -55x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -55x + x2 = 0 + -4
-55x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-55x + x2 = -4

The x term is -55x.  Take half its coefficient (-27.5).
Square it (756.25) and add it to both sides.

Add '756.25' to each side of the equation.
-55x + 756.25 + x2 = -4 + 756.25

Reorder the terms:
756.25 + -55x + x2 = -4 + 756.25

Combine like terms: -4 + 756.25 = 752.25
756.25 + -55x + x2 = 752.25

Factor a perfect square on the left side:
(x + -27.5)(x + -27.5) = 752.25

Calculate the square root of the right side: 27.427176304

Break this problem into two subproblems by setting 
(x + -27.5) equal to 27.427176304 and -27.427176304.

Subproblem 1
x + -27.5 = 27.427176304

Simplifying
x + -27.5 = 27.427176304

Reorder the terms:
-27.5 + x = 27.427176304

Solving
-27.5 + x = 27.427176304

Solving for variable 'x'.

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

Add '27.5' to each side of the equation.
-27.5 + 27.5 + x = 27.427176304 + 27.5

Combine like terms: -27.5 + 27.5 = 0.0
0.0 + x = 27.427176304 + 27.5
x = 27.427176304 + 27.5

Combine like terms: 27.427176304 + 27.5 = 54.927176304
x = 54.927176304

Simplifying
x = 54.927176304

Subproblem 2
x + -27.5 = -27.427176304

Simplifying
x + -27.5 = -27.427176304

Reorder the terms:
-27.5 + x = -27.427176304

Solving
-27.5 + x = -27.427176304

Solving for variable 'x'.

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

Add '27.5' to each side of the equation.
-27.5 + 27.5 + x = -27.427176304 + 27.5

Combine like terms: -27.5 + 27.5 = 0.0
0.0 + x = -27.427176304 + 27.5
x = -27.427176304 + 27.5

Combine like terms: -27.427176304 + 27.5 = 0.072823696
x = 0.072823696

Simplifying
x = 0.072823696

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {54.927176304, 0.072823696}