5776(t)=-16t^2+5776

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Solution for 5776(t)=-16t^2+5776 equation: 


Simplifying
5776(t) = -16t2 + 5776

Reorder the terms:
5776t = 5776 + -16t2

Solving
5776t = 5776 + -16t2

Solving for variable 't'.

Reorder the terms:
-5776 + 5776t + 16t2 = 5776 + -16t2 + -5776 + 16t2

Reorder the terms:
-5776 + 5776t + 16t2 = 5776 + -5776 + -16t2 + 16t2

Combine like terms: 5776 + -5776 = 0
-5776 + 5776t + 16t2 = 0 + -16t2 + 16t2
-5776 + 5776t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-5776 + 5776t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-361 + 361t + t2) = 0

Ignore the factor 16.

Subproblem 1
Set the factor '(-361 + 361t + t2)' equal to zero and attempt to solve:

Simplifying
-361 + 361t + t2 = 0

Solving
-361 + 361t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '361' to each side of the equation.
-361 + 361t + 361 + t2 = 0 + 361

Reorder the terms:
-361 + 361 + 361t + t2 = 0 + 361

Combine like terms: -361 + 361 = 0
0 + 361t + t2 = 0 + 361
361t + t2 = 0 + 361

Combine like terms: 0 + 361 = 361
361t + t2 = 361

The t term is 361t.  Take half its coefficient (180.5).
Square it (32580.25) and add it to both sides.

Add '32580.25' to each side of the equation.
361t + 32580.25 + t2 = 361 + 32580.25

Reorder the terms:
32580.25 + 361t + t2 = 361 + 32580.25

Combine like terms: 361 + 32580.25 = 32941.25
32580.25 + 361t + t2 = 32941.25

Factor a perfect square on the left side:
(t + 180.5)(t + 180.5) = 32941.25

Calculate the square root of the right side: 181.497245158

Break this problem into two subproblems by setting 
(t + 180.5) equal to 181.497245158 and -181.497245158.


Subproblem 1
t + 180.5 = 181.497245158

Simplifying
t + 180.5 = 181.497245158

Reorder the terms:
180.5 + t = 181.497245158

Solving
180.5 + t = 181.497245158

Solving for variable 't'.

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

Add '-180.5' to each side of the equation.
180.5 + -180.5 + t = 181.497245158 + -180.5

Combine like terms: 180.5 + -180.5 = 0.0
0.0 + t = 181.497245158 + -180.5
t = 181.497245158 + -180.5

Combine like terms: 181.497245158 + -180.5 = 0.997245158
t = 0.997245158

Simplifying
t = 0.997245158


Subproblem 2
t + 180.5 = -181.497245158

Simplifying
t + 180.5 = -181.497245158

Reorder the terms:
180.5 + t = -181.497245158

Solving
180.5 + t = -181.497245158

Solving for variable 't'.

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

Add '-180.5' to each side of the equation.
180.5 + -180.5 + t = -181.497245158 + -180.5

Combine like terms: 180.5 + -180.5 = 0.0
0.0 + t = -181.497245158 + -180.5
t = -181.497245158 + -180.5

Combine like terms: -181.497245158 + -180.5 = -361.997245158
t = -361.997245158

Simplifying
t = -361.997245158


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.997245158, -361.997245158}
Solution
t = {0.997245158, -361.997245158}

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