k^2+7k-23=0

Solution for k^2+7k-23=0 equation:

Simplifying
k2 + 7k + -23 = 0

Reorder the terms:
-23 + 7k + k2 = 0

Solving
-23 + 7k + k2 = 0

Solving for variable 'k'.

Begin completing the square.

Move the constant term to the right:

Add '23' to each side of the equation.
-23 + 7k + 23 + k2 = 0 + 23

Reorder the terms:
-23 + 23 + 7k + k2 = 0 + 23

Combine like terms: -23 + 23 = 0
0 + 7k + k2 = 0 + 23
7k + k2 = 0 + 23

Combine like terms: 0 + 23 = 23
7k + k2 = 23

The k term is 7k.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7k + 12.25 + k2 = 23 + 12.25

Reorder the terms:
12.25 + 7k + k2 = 23 + 12.25

Combine like terms: 23 + 12.25 = 35.25
12.25 + 7k + k2 = 35.25

Factor a perfect square on the left side:
(k + 3.5)(k + 3.5) = 35.25

Calculate the square root of the right side: 5.937171044

Break this problem into two subproblems by setting 
(k + 3.5) equal to 5.937171044 and -5.937171044.

Subproblem 1
k + 3.5 = 5.937171044

Simplifying
k + 3.5 = 5.937171044

Reorder the terms:
3.5 + k = 5.937171044

Solving
3.5 + k = 5.937171044

Solving for variable 'k'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + k = 5.937171044 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + k = 5.937171044 + -3.5
k = 5.937171044 + -3.5

Combine like terms: 5.937171044 + -3.5 = 2.437171044
k = 2.437171044

Simplifying
k = 2.437171044

Subproblem 2
k + 3.5 = -5.937171044

Simplifying
k + 3.5 = -5.937171044

Reorder the terms:
3.5 + k = -5.937171044

Solving
3.5 + k = -5.937171044

Solving for variable 'k'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + k = -5.937171044 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + k = -5.937171044 + -3.5
k = -5.937171044 + -3.5

Combine like terms: -5.937171044 + -3.5 = -9.437171044
k = -9.437171044

Simplifying
k = -9.437171044

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {2.437171044, -9.437171044}