t^2-23t-23=0

Solution for t^2-23t-23=0 equation:

Simplifying
t2 + -23t + -23 = 0

Reorder the terms:
-23 + -23t + t2 = 0

Solving
-23 + -23t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '23' to each side of the equation.
-23 + -23t + 23 + t2 = 0 + 23

Reorder the terms:
-23 + 23 + -23t + t2 = 0 + 23

Combine like terms: -23 + 23 = 0
0 + -23t + t2 = 0 + 23
-23t + t2 = 0 + 23

Combine like terms: 0 + 23 = 23
-23t + t2 = 23

The t term is -23t.  Take half its coefficient (-11.5).
Square it (132.25) and add it to both sides.

Add '132.25' to each side of the equation.
-23t + 132.25 + t2 = 23 + 132.25

Reorder the terms:
132.25 + -23t + t2 = 23 + 132.25

Combine like terms: 23 + 132.25 = 155.25
132.25 + -23t + t2 = 155.25

Factor a perfect square on the left side:
(t + -11.5)(t + -11.5) = 155.25

Calculate the square root of the right side: 12.459935794

Break this problem into two subproblems by setting 
(t + -11.5) equal to 12.459935794 and -12.459935794.

Subproblem 1
t + -11.5 = 12.459935794

Simplifying
t + -11.5 = 12.459935794

Reorder the terms:
-11.5 + t = 12.459935794

Solving
-11.5 + t = 12.459935794

Solving for variable 't'.

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

Add '11.5' to each side of the equation.
-11.5 + 11.5 + t = 12.459935794 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + t = 12.459935794 + 11.5
t = 12.459935794 + 11.5

Combine like terms: 12.459935794 + 11.5 = 23.959935794
t = 23.959935794

Simplifying
t = 23.959935794

Subproblem 2
t + -11.5 = -12.459935794

Simplifying
t + -11.5 = -12.459935794

Reorder the terms:
-11.5 + t = -12.459935794

Solving
-11.5 + t = -12.459935794

Solving for variable 't'.

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

Add '11.5' to each side of the equation.
-11.5 + 11.5 + t = -12.459935794 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + t = -12.459935794 + 11.5
t = -12.459935794 + 11.5

Combine like terms: -12.459935794 + 11.5 = -0.959935794
t = -0.959935794

Simplifying
t = -0.959935794

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {23.959935794, -0.959935794}