x^2+1x-127=0

Solution for x^2+1x-127=0 equation:

Simplifying
x2 + 1x + -127 = 0

Reorder the terms:
-127 + 1x + x2 = 0

Solving
-127 + 1x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '127' to each side of the equation.
-127 + 1x + 127 + x2 = 0 + 127

Reorder the terms:
-127 + 127 + 1x + x2 = 0 + 127

Combine like terms: -127 + 127 = 0
0 + 1x + x2 = 0 + 127
1x + x2 = 0 + 127

Combine like terms: 0 + 127 = 127
1x + x2 = 127

The x term is 1x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 127 + 0.25

Reorder the terms:
0.25 + x + x2 = 127 + 0.25

Combine like terms: 127 + 0.25 = 127.25
0.25 + x + x2 = 127.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 127.25

Calculate the square root of the right side: 11.280514173

Break this problem into two subproblems by setting 
(x + 0.5) equal to 11.280514173 and -11.280514173.

Subproblem 1
x + 0.5 = 11.280514173

Simplifying
x + 0.5 = 11.280514173

Reorder the terms:
0.5 + x = 11.280514173

Solving
0.5 + x = 11.280514173

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 11.280514173 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 11.280514173 + -0.5
x = 11.280514173 + -0.5

Combine like terms: 11.280514173 + -0.5 = 10.780514173
x = 10.780514173

Simplifying
x = 10.780514173

Subproblem 2
x + 0.5 = -11.280514173

Simplifying
x + 0.5 = -11.280514173

Reorder the terms:
0.5 + x = -11.280514173

Solving
0.5 + x = -11.280514173

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -11.280514173 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -11.280514173 + -0.5
x = -11.280514173 + -0.5

Combine like terms: -11.280514173 + -0.5 = -11.780514173
x = -11.780514173

Simplifying
x = -11.780514173

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.780514173, -11.780514173}