-16t^2+16t=2.56

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Solution for -16t^2+16t=2.56 equation: 


Simplifying
-16t2 + 16t = 2.56

Reorder the terms:
16t + -16t2 = 2.56

Solving
16t + -16t2 = 2.56

Solving for variable 't'.

Reorder the terms:
-2.56 + 16t + -16t2 = 2.56 + -2.56

Combine like terms: 2.56 + -2.56 = 0.00
-2.56 + 16t + -16t2 = 0.00

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
0.16 + -1t + t2 = 0.00

Move the constant term to the right:

Add '-0.16' to each side of the equation.
0.16 + -1t + -0.16 + t2 = 0.00 + -0.16

Reorder the terms:
0.16 + -0.16 + -1t + t2 = 0.00 + -0.16

Combine like terms: 0.16 + -0.16 = 0.00
0.00 + -1t + t2 = 0.00 + -0.16
-1t + t2 = 0.00 + -0.16

Combine like terms: 0.00 + -0.16 = -0.16
-1t + t2 = -0.16

The t term is -1t.  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.
-1t + 0.25 + t2 = -0.16 + 0.25

Reorder the terms:
0.25 + -1t + t2 = -0.16 + 0.25

Combine like terms: -0.16 + 0.25 = 0.09
0.25 + -1t + t2 = 0.09

Factor a perfect square on the left side:
(t + -0.5)(t + -0.5) = 0.09

Calculate the square root of the right side: 0.3

Break this problem into two subproblems by setting 
(t + -0.5) equal to 0.3 and -0.3.


Subproblem 1
t + -0.5 = 0.3

Simplifying
t + -0.5 = 0.3

Reorder the terms:
-0.5 + t = 0.3

Solving
-0.5 + t = 0.3

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 = 0.3 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + t = 0.3 + 0.5
t = 0.3 + 0.5

Combine like terms: 0.3 + 0.5 = 0.8
t = 0.8

Simplifying
t = 0.8


Subproblem 2
t + -0.5 = -0.3

Simplifying
t + -0.5 = -0.3

Reorder the terms:
-0.5 + t = -0.3

Solving
-0.5 + t = -0.3

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 = -0.3 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + t = -0.3 + 0.5
t = -0.3 + 0.5

Combine like terms: -0.3 + 0.5 = 0.2
t = 0.2

Simplifying
t = 0.2


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.8, 0.2}

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