100=t^2+t

Solution for 100=t^2+t equation:

Simplifying
100 = t2 + t

Reorder the terms:
100 = t + t2

Solving
100 = t + t2

Solving for variable 't'.

Reorder the terms:
100 + -1t + -1t2 = t + -1t + t2 + -1t2

Combine like terms: t + -1t = 0
100 + -1t + -1t2 = 0 + t2 + -1t2
100 + -1t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
100 + -1t + -1t2 = 0

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

Divide each side by '-1'.
-100 + t + t2 = 0

Move the constant term to the right:

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

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

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

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

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 = 100 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + t2 = 100 + 0.25

Combine like terms: 100 + 0.25 = 100.25
1.25 + t2 = 100.25

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = 100.25

Calculate the square root of the right side: 10.012492197

Break this problem into two subproblems by setting 
(t + 0.5) equal to 10.012492197 and -10.012492197.

Subproblem 1
t + 0.5 = 10.012492197

Simplifying
t + 0.5 = 10.012492197

Reorder the terms:
0.5 + t = 10.012492197

Solving
0.5 + t = 10.012492197

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 = 10.012492197 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = 10.012492197 + -0.5
t = 10.012492197 + -0.5

Combine like terms: 10.012492197 + -0.5 = 9.512492197
t = 9.512492197

Simplifying
t = 9.512492197

Subproblem 2
t + 0.5 = -10.012492197

Simplifying
t + 0.5 = -10.012492197

Reorder the terms:
0.5 + t = -10.012492197

Solving
0.5 + t = -10.012492197

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 = -10.012492197 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = -10.012492197 + -0.5
t = -10.012492197 + -0.5

Combine like terms: -10.012492197 + -0.5 = -10.512492197
t = -10.512492197

Simplifying
t = -10.512492197

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {9.512492197, -10.512492197}