-t^2+t+33=0

Solution for -t^2+t+33=0 equation:

Simplifying
-1t2 + t + 33 = 0

Reorder the terms:
33 + t + -1t2 = 0

Solving
33 + t + -1t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-33 + -1t + t2 = 0

Move the constant term to the right:

Add '33' to each side of the equation.
-33 + -1t + 33 + t2 = 0 + 33

Reorder the terms:
-33 + 33 + -1t + t2 = 0 + 33

Combine like terms: -33 + 33 = 0
0 + -1t + t2 = 0 + 33
-1t + t2 = 0 + 33

Combine like terms: 0 + 33 = 33
-1t + t2 = 33

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

Add '0.25' to each side of the equation.
-1t + 0.25 + t2 = 33 + 0.25

Reorder the terms:
0.25 + -1t + t2 = 33 + 0.25

Combine like terms: 33 + 0.25 = 33.25
0.25 + -1t + t2 = 33.25

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = 33.25

Calculate the square root of the right side: 5.766281297

Break this problem into two subproblems by setting 
(t + 0.5) equal to 5.766281297 and -5.766281297.

Subproblem 1
t + 0.5 = 5.766281297

Simplifying
t + 0.5 = 5.766281297

Reorder the terms:
0.5 + t = 5.766281297

Solving
0.5 + t = 5.766281297

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = 5.766281297 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = 5.766281297 + -0.5
t = 5.766281297 + -0.5

Combine like terms: 5.766281297 + -0.5 = 5.266281297
t = 5.266281297

Simplifying
t = 5.266281297

Subproblem 2
t + 0.5 = -5.766281297

Simplifying
t + 0.5 = -5.766281297

Reorder the terms:
0.5 + t = -5.766281297

Solving
0.5 + t = -5.766281297

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = -5.766281297 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = -5.766281297 + -0.5
t = -5.766281297 + -0.5

Combine like terms: -5.766281297 + -0.5 = -6.266281297
t = -6.266281297

Simplifying
t = -6.266281297

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {5.266281297, -6.266281297}