16=t+t^2

Solution for 16=t+t^2 equation:

Simplifying
16 = t + t2

Solving
16 = t + t2

Solving for variable 't'.

Reorder the terms:
16 + -1t + -1t2 = t + -1t + t2 + -1t2

Combine like terms: t + -1t = 0
16 + -1t + -1t2 = 0 + t2 + -1t2
16 + -1t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
16 + -1t + -1t2 = 0

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

Divide each side by '-1'.
-16 + t + t2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + t + 16 + t2 = 0 + 16

Reorder the terms:
-16 + 16 + t + t2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + t + t2 = 0 + 16
t + t2 = 0 + 16

Combine like terms: 0 + 16 = 16
t + t2 = 16

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.
 + 0.25 + t2 = 16 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + t2 = 16 + 0.25

Combine like terms: 16 + 0.25 = 16.25
1.25 + t2 = 16.25

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = 16.25

Calculate the square root of the right side: 4.031128874

Break this problem into two subproblems by setting 
(t + 0.5) equal to 4.031128874 and -4.031128874.

Subproblem 1
t + 0.5 = 4.031128874

Simplifying
t + 0.5 = 4.031128874

Reorder the terms:
0.5 + t = 4.031128874

Solving
0.5 + t = 4.031128874

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 = 4.031128874 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = 4.031128874 + -0.5
t = 4.031128874 + -0.5

Combine like terms: 4.031128874 + -0.5 = 3.531128874
t = 3.531128874

Simplifying
t = 3.531128874

Subproblem 2
t + 0.5 = -4.031128874

Simplifying
t + 0.5 = -4.031128874

Reorder the terms:
0.5 + t = -4.031128874

Solving
0.5 + t = -4.031128874

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 = -4.031128874 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = -4.031128874 + -0.5
t = -4.031128874 + -0.5

Combine like terms: -4.031128874 + -0.5 = -4.531128874
t = -4.531128874

Simplifying
t = -4.531128874

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.531128874, -4.531128874}