2.6=t+t^2

Solution for 2.6=t+t^2 equation:

Simplifying
2.6 = t + t2

Solving
2.6 = t + t2

Solving for variable 't'.

Reorder the terms:
2.6 + -1t + -1t2 = t + -1t + t2 + -1t2

Combine like terms: t + -1t = 0
2.6 + -1t + -1t2 = 0 + t2 + -1t2
2.6 + -1t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
2.6 + -1t + -1t2 = 0

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

Divide each side by '-1'.
-2.6 + t + t2 = 0

Move the constant term to the right:

Add '2.6' to each side of the equation.
-2.6 + t + 2.6 + t2 = 0 + 2.6

Reorder the terms:
-2.6 + 2.6 + t + t2 = 0 + 2.6

Combine like terms: -2.6 + 2.6 = 0.0
0.0 + t + t2 = 0 + 2.6
t + t2 = 0 + 2.6

Combine like terms: 0 + 2.6 = 2.6
t + t2 = 2.6

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 = 2.6 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + t2 = 2.6 + 0.25

Combine like terms: 2.6 + 0.25 = 2.85
1.25 + t2 = 2.85

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = 2.85

Calculate the square root of the right side: 1.688194302

Break this problem into two subproblems by setting 
(t + 0.5) equal to 1.688194302 and -1.688194302.

Subproblem 1
t + 0.5 = 1.688194302

Simplifying
t + 0.5 = 1.688194302

Reorder the terms:
0.5 + t = 1.688194302

Solving
0.5 + t = 1.688194302

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 = 1.688194302 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = 1.688194302 + -0.5
t = 1.688194302 + -0.5

Combine like terms: 1.688194302 + -0.5 = 1.188194302
t = 1.188194302

Simplifying
t = 1.188194302

Subproblem 2
t + 0.5 = -1.688194302

Simplifying
t + 0.5 = -1.688194302

Reorder the terms:
0.5 + t = -1.688194302

Solving
0.5 + t = -1.688194302

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 = -1.688194302 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = -1.688194302 + -0.5
t = -1.688194302 + -0.5

Combine like terms: -1.688194302 + -0.5 = -2.188194302
t = -2.188194302

Simplifying
t = -2.188194302

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.188194302, -2.188194302}