t^2-23t+50=-50

Solution for t^2-23t+50=-50 equation:

Simplifying
t2 + -23t + 50 = -50

Reorder the terms:
50 + -23t + t2 = -50

Solving
50 + -23t + t2 = -50

Solving for variable 't'.

Reorder the terms:
50 + 50 + -23t + t2 = -50 + 50

Combine like terms: 50 + 50 = 100
100 + -23t + t2 = -50 + 50

Combine like terms: -50 + 50 = 0
100 + -23t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-100' to each side of the equation.
100 + -23t + -100 + t2 = 0 + -100

Reorder the terms:
100 + -100 + -23t + t2 = 0 + -100

Combine like terms: 100 + -100 = 0
0 + -23t + t2 = 0 + -100
-23t + t2 = 0 + -100

Combine like terms: 0 + -100 = -100
-23t + t2 = -100

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 = -100 + 132.25

Reorder the terms:
132.25 + -23t + t2 = -100 + 132.25

Combine like terms: -100 + 132.25 = 32.25
132.25 + -23t + t2 = 32.25

Factor a perfect square on the left side:
(t + -11.5)(t + -11.5) = 32.25

Calculate the square root of the right side: 5.678908346

Break this problem into two subproblems by setting 
(t + -11.5) equal to 5.678908346 and -5.678908346.

Subproblem 1
t + -11.5 = 5.678908346

Simplifying
t + -11.5 = 5.678908346

Reorder the terms:
-11.5 + t = 5.678908346

Solving
-11.5 + t = 5.678908346

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 = 5.678908346 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + t = 5.678908346 + 11.5
t = 5.678908346 + 11.5

Combine like terms: 5.678908346 + 11.5 = 17.178908346
t = 17.178908346

Simplifying
t = 17.178908346

Subproblem 2
t + -11.5 = -5.678908346

Simplifying
t + -11.5 = -5.678908346

Reorder the terms:
-11.5 + t = -5.678908346

Solving
-11.5 + t = -5.678908346

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 = -5.678908346 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + t = -5.678908346 + 11.5
t = -5.678908346 + 11.5

Combine like terms: -5.678908346 + 11.5 = 5.821091654
t = 5.821091654

Simplifying
t = 5.821091654

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {17.178908346, 5.821091654}