2x^2+1x-23=0

Solution for 2x^2+1x-23=0 equation:

Simplifying
2x2 + 1x + -23 = 0

Reorder the terms:
-23 + 1x + 2x2 = 0

Solving
-23 + 1x + 2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-11.5 + 0.5x + x2 = 0

Move the constant term to the right:

Add '11.5' to each side of the equation.
-11.5 + 0.5x + 11.5 + x2 = 0 + 11.5

Reorder the terms:
-11.5 + 11.5 + 0.5x + x2 = 0 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + 0.5x + x2 = 0 + 11.5
0.5x + x2 = 0 + 11.5

Combine like terms: 0 + 11.5 = 11.5
0.5x + x2 = 11.5

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 11.5 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 11.5 + 0.0625

Combine like terms: 11.5 + 0.0625 = 11.5625
0.0625 + 0.5x + x2 = 11.5625

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 11.5625

Calculate the square root of the right side: 3.400367627

Break this problem into two subproblems by setting 
(x + 0.25) equal to 3.400367627 and -3.400367627.

Subproblem 1
x + 0.25 = 3.400367627

Simplifying
x + 0.25 = 3.400367627

Reorder the terms:
0.25 + x = 3.400367627

Solving
0.25 + x = 3.400367627

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 3.400367627 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 3.400367627 + -0.25
x = 3.400367627 + -0.25

Combine like terms: 3.400367627 + -0.25 = 3.150367627
x = 3.150367627

Simplifying
x = 3.150367627

Subproblem 2
x + 0.25 = -3.400367627

Simplifying
x + 0.25 = -3.400367627

Reorder the terms:
0.25 + x = -3.400367627

Solving
0.25 + x = -3.400367627

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -3.400367627 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -3.400367627 + -0.25
x = -3.400367627 + -0.25

Combine like terms: -3.400367627 + -0.25 = -3.650367627
x = -3.650367627

Simplifying
x = -3.650367627

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.150367627, -3.650367627}