5t^2=1-5t

Solution for 5t^2=1-5t equation:

Simplifying
5t2 = 1 + -5t

Solving
5t2 = 1 + -5t

Solving for variable 't'.

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

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

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

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

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

Divide each side by '5'.
-0.2 + t + t2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + t + 0.2 + t2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + t + t2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + t + t2 = 0 + 0.2
t + t2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
t + t2 = 0.2

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 = 0.2 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + t2 = 0.2 + 0.25

Combine like terms: 0.2 + 0.25 = 0.45
1.25 + t2 = 0.45

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = 0.45

Calculate the square root of the right side: 0.670820393

Break this problem into two subproblems by setting 
(t + 0.5) equal to 0.670820393 and -0.670820393.

Subproblem 1
t + 0.5 = 0.670820393

Simplifying
t + 0.5 = 0.670820393

Reorder the terms:
0.5 + t = 0.670820393

Solving
0.5 + t = 0.670820393

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 = 0.670820393 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = 0.670820393 + -0.5
t = 0.670820393 + -0.5

Combine like terms: 0.670820393 + -0.5 = 0.170820393
t = 0.170820393

Simplifying
t = 0.170820393

Subproblem 2
t + 0.5 = -0.670820393

Simplifying
t + 0.5 = -0.670820393

Reorder the terms:
0.5 + t = -0.670820393

Solving
0.5 + t = -0.670820393

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 = -0.670820393 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = -0.670820393 + -0.5
t = -0.670820393 + -0.5

Combine like terms: -0.670820393 + -0.5 = -1.170820393
t = -1.170820393

Simplifying
t = -1.170820393

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.170820393, -1.170820393}