t*t+t=2000

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Solution for t*t+t=2000 equation: 


Simplifying
t * t + t = 2000

Multiply t * t
t2 + t = 2000

Reorder the terms:
t + t2 = 2000

Solving
t + t2 = 2000

Solving for variable 't'.

Reorder the terms:
-2000 + t + t2 = 2000 + -2000

Combine like terms: 2000 + -2000 = 0
-2000 + t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2000' to each side of the equation.
-2000 + t + 2000 + t2 = 0 + 2000

Reorder the terms:
-2000 + 2000 + t + t2 = 0 + 2000

Combine like terms: -2000 + 2000 = 0
0 + t + t2 = 0 + 2000
t + t2 = 0 + 2000

Combine like terms: 0 + 2000 = 2000
t + t2 = 2000

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 = 2000 + 0.25

Reorder the terms:
0.25 + t + t2 = 2000 + 0.25

Combine like terms: 2000 + 0.25 = 2000.25
0.25 + t + t2 = 2000.25

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = 2000.25

Calculate the square root of the right side: 44.724154548

Break this problem into two subproblems by setting 
(t + 0.5) equal to 44.724154548 and -44.724154548.


Subproblem 1
t + 0.5 = 44.724154548

Simplifying
t + 0.5 = 44.724154548

Reorder the terms:
0.5 + t = 44.724154548

Solving
0.5 + t = 44.724154548

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 = 44.724154548 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = 44.724154548 + -0.5
t = 44.724154548 + -0.5

Combine like terms: 44.724154548 + -0.5 = 44.224154548
t = 44.224154548

Simplifying
t = 44.224154548


Subproblem 2
t + 0.5 = -44.724154548

Simplifying
t + 0.5 = -44.724154548

Reorder the terms:
0.5 + t = -44.724154548

Solving
0.5 + t = -44.724154548

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 = -44.724154548 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = -44.724154548 + -0.5
t = -44.724154548 + -0.5

Combine like terms: -44.724154548 + -0.5 = -45.224154548
t = -45.224154548

Simplifying
t = -45.224154548


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {44.224154548, -45.224154548}

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