t=-t^2+5

Solution for t=-t^2+5 equation:

Simplifying
t = -1t2 + 5

Reorder the terms:
t = 5 + -1t2

Solving
t = 5 + -1t2

Solving for variable 't'.

Reorder the terms:
-5 + t + t2 = 5 + -1t2 + -5 + t2

Reorder the terms:
-5 + t + t2 = 5 + -5 + -1t2 + t2

Combine like terms: 5 + -5 = 0
-5 + t + t2 = 0 + -1t2 + t2
-5 + t + t2 = -1t2 + t2

Combine like terms: -1t2 + t2 = 0
-5 + t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + t + 5 + t2 = 0 + 5

Reorder the terms:
-5 + 5 + t + t2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + t + t2 = 0 + 5
t + t2 = 0 + 5

Combine like terms: 0 + 5 = 5
t + t2 = 5

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.
t + 0.25 + t2 = 5 + 0.25

Reorder the terms:
0.25 + t + t2 = 5 + 0.25

Combine like terms: 5 + 0.25 = 5.25
0.25 + t + t2 = 5.25

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(t + 0.5) equal to 2.291287847 and -2.291287847.

Subproblem 1
t + 0.5 = 2.291287847

Simplifying
t + 0.5 = 2.291287847

Reorder the terms:
0.5 + t = 2.291287847

Solving
0.5 + t = 2.291287847

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 = 2.291287847 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = 2.291287847 + -0.5
t = 2.291287847 + -0.5

Combine like terms: 2.291287847 + -0.5 = 1.791287847
t = 1.791287847

Simplifying
t = 1.791287847

Subproblem 2
t + 0.5 = -2.291287847

Simplifying
t + 0.5 = -2.291287847

Reorder the terms:
0.5 + t = -2.291287847

Solving
0.5 + t = -2.291287847

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 = -2.291287847 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = -2.291287847 + -0.5
t = -2.291287847 + -0.5

Combine like terms: -2.291287847 + -0.5 = -2.791287847
t = -2.791287847

Simplifying
t = -2.791287847

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.791287847, -2.791287847}