x^2+4x-23=0

Solution for x^2+4x-23=0 equation:

Simplifying
x2 + 4x + -23 = 0

Reorder the terms:
-23 + 4x + x2 = 0

Solving
-23 + 4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '23' to each side of the equation.
-23 + 4x + 23 + x2 = 0 + 23

Reorder the terms:
-23 + 23 + 4x + x2 = 0 + 23

Combine like terms: -23 + 23 = 0
0 + 4x + x2 = 0 + 23
4x + x2 = 0 + 23

Combine like terms: 0 + 23 = 23
4x + x2 = 23

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 23 + 4

Reorder the terms:
4 + 4x + x2 = 23 + 4

Combine like terms: 23 + 4 = 27
4 + 4x + x2 = 27

Factor a perfect square on the left side:
(x + 2)(x + 2) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(x + 2) equal to 5.196152423 and -5.196152423.

Subproblem 1
x + 2 = 5.196152423

Simplifying
x + 2 = 5.196152423

Reorder the terms:
2 + x = 5.196152423

Solving
2 + x = 5.196152423

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 5.196152423 + -2

Combine like terms: 2 + -2 = 0
0 + x = 5.196152423 + -2
x = 5.196152423 + -2

Combine like terms: 5.196152423 + -2 = 3.196152423
x = 3.196152423

Simplifying
x = 3.196152423

Subproblem 2
x + 2 = -5.196152423

Simplifying
x + 2 = -5.196152423

Reorder the terms:
2 + x = -5.196152423

Solving
2 + x = -5.196152423

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -5.196152423 + -2

Combine like terms: 2 + -2 = 0
0 + x = -5.196152423 + -2
x = -5.196152423 + -2

Combine like terms: -5.196152423 + -2 = -7.196152423
x = -7.196152423

Simplifying
x = -7.196152423

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.196152423, -7.196152423}