256=-16t^2+256t

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Solution for 256=-16t^2+256t equation: 


Simplifying
256 = -16t2 + 256t

Reorder the terms:
256 = 256t + -16t2

Solving
256 = 256t + -16t2

Solving for variable 't'.

Reorder the terms:
256 + -256t + 16t2 = 256t + -256t + -16t2 + 16t2

Combine like terms: 256t + -256t = 0
256 + -256t + 16t2 = 0 + -16t2 + 16t2
256 + -256t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
256 + -256t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(16 + -16t + t2) = 0

Ignore the factor 16.

Subproblem 1
Set the factor '(16 + -16t + t2)' equal to zero and attempt to solve:

Simplifying
16 + -16t + t2 = 0

Solving
16 + -16t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + -16t + -16 + t2 = 0 + -16

Reorder the terms:
16 + -16 + -16t + t2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -16t + t2 = 0 + -16
-16t + t2 = 0 + -16

Combine like terms: 0 + -16 = -16
-16t + t2 = -16

The t term is -16t.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16t + 64 + t2 = -16 + 64

Reorder the terms:
64 + -16t + t2 = -16 + 64

Combine like terms: -16 + 64 = 48
64 + -16t + t2 = 48

Factor a perfect square on the left side:
(t + -8)(t + -8) = 48

Calculate the square root of the right side: 6.92820323

Break this problem into two subproblems by setting 
(t + -8) equal to 6.92820323 and -6.92820323.


Subproblem 1
t + -8 = 6.92820323

Simplifying
t + -8 = 6.92820323

Reorder the terms:
-8 + t = 6.92820323

Solving
-8 + t = 6.92820323

Solving for variable 't'.

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

Add '8' to each side of the equation.
-8 + 8 + t = 6.92820323 + 8

Combine like terms: -8 + 8 = 0
0 + t = 6.92820323 + 8
t = 6.92820323 + 8

Combine like terms: 6.92820323 + 8 = 14.92820323
t = 14.92820323

Simplifying
t = 14.92820323


Subproblem 2
t + -8 = -6.92820323

Simplifying
t + -8 = -6.92820323

Reorder the terms:
-8 + t = -6.92820323

Solving
-8 + t = -6.92820323

Solving for variable 't'.

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

Add '8' to each side of the equation.
-8 + 8 + t = -6.92820323 + 8

Combine like terms: -8 + 8 = 0
0 + t = -6.92820323 + 8
t = -6.92820323 + 8

Combine like terms: -6.92820323 + 8 = 1.07179677
t = 1.07179677

Simplifying
t = 1.07179677


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {14.92820323, 1.07179677}
Solution
t = {14.92820323, 1.07179677}

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