10t-5t^2=2

Solution for 10t-5t^2=2 equation:

Simplifying
10t + -5t2 = 2

Solving
10t + -5t2 = 2

Solving for variable 't'.

Reorder the terms:
-2 + 10t + -5t2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 10t + -5t2 = 0

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

Divide each side by '-5'.
0.4 + -2t + t2 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + -2t + -0.4 + t2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + -2t + t2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + -2t + t2 = 0 + -0.4
-2t + t2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
-2t + t2 = -0.4

The t term is -2t.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2t + 1 + t2 = -0.4 + 1

Reorder the terms:
1 + -2t + t2 = -0.4 + 1

Combine like terms: -0.4 + 1 = 0.6
1 + -2t + t2 = 0.6

Factor a perfect square on the left side:
(t + -1)(t + -1) = 0.6

Calculate the square root of the right side: 0.774596669

Break this problem into two subproblems by setting 
(t + -1) equal to 0.774596669 and -0.774596669.

Subproblem 1
t + -1 = 0.774596669

Simplifying
t + -1 = 0.774596669

Reorder the terms:
-1 + t = 0.774596669

Solving
-1 + t = 0.774596669

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + t = 0.774596669 + 1

Combine like terms: -1 + 1 = 0
0 + t = 0.774596669 + 1
t = 0.774596669 + 1

Combine like terms: 0.774596669 + 1 = 1.774596669
t = 1.774596669

Simplifying
t = 1.774596669

Subproblem 2
t + -1 = -0.774596669

Simplifying
t + -1 = -0.774596669

Reorder the terms:
-1 + t = -0.774596669

Solving
-1 + t = -0.774596669

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + t = -0.774596669 + 1

Combine like terms: -1 + 1 = 0
0 + t = -0.774596669 + 1
t = -0.774596669 + 1

Combine like terms: -0.774596669 + 1 = 0.225403331
t = 0.225403331

Simplifying
t = 0.225403331

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.774596669, 0.225403331}