-16t^2+76t+1444=0

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Solution for -16t^2+76t+1444=0 equation: 


Simplifying
-16t2 + 76t + 1444 = 0

Reorder the terms:
1444 + 76t + -16t2 = 0

Solving
1444 + 76t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(361 + 19t + -4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(361 + 19t + -4t2)' equal to zero and attempt to solve:

Simplifying
361 + 19t + -4t2 = 0

Solving
361 + 19t + -4t2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-90.25 + -4.75t + t2 = 0

Move the constant term to the right:

Add '90.25' to each side of the equation.
-90.25 + -4.75t + 90.25 + t2 = 0 + 90.25

Reorder the terms:
-90.25 + 90.25 + -4.75t + t2 = 0 + 90.25

Combine like terms: -90.25 + 90.25 = 0.00
0.00 + -4.75t + t2 = 0 + 90.25
-4.75t + t2 = 0 + 90.25

Combine like terms: 0 + 90.25 = 90.25
-4.75t + t2 = 90.25

The t term is -4.75t.  Take half its coefficient (-2.375).
Square it (5.640625) and add it to both sides.

Add '5.640625' to each side of the equation.
-4.75t + 5.640625 + t2 = 90.25 + 5.640625

Reorder the terms:
5.640625 + -4.75t + t2 = 90.25 + 5.640625

Combine like terms: 90.25 + 5.640625 = 95.890625
5.640625 + -4.75t + t2 = 95.890625

Factor a perfect square on the left side:
(t + -2.375)(t + -2.375) = 95.890625

Calculate the square root of the right side: 9.792375861

Break this problem into two subproblems by setting 
(t + -2.375) equal to 9.792375861 and -9.792375861.


Subproblem 1
t + -2.375 = 9.792375861

Simplifying
t + -2.375 = 9.792375861

Reorder the terms:
-2.375 + t = 9.792375861

Solving
-2.375 + t = 9.792375861

Solving for variable 't'.

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

Add '2.375' to each side of the equation.
-2.375 + 2.375 + t = 9.792375861 + 2.375

Combine like terms: -2.375 + 2.375 = 0.000
0.000 + t = 9.792375861 + 2.375
t = 9.792375861 + 2.375

Combine like terms: 9.792375861 + 2.375 = 12.167375861
t = 12.167375861

Simplifying
t = 12.167375861


Subproblem 2
t + -2.375 = -9.792375861

Simplifying
t + -2.375 = -9.792375861

Reorder the terms:
-2.375 + t = -9.792375861

Solving
-2.375 + t = -9.792375861

Solving for variable 't'.

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

Add '2.375' to each side of the equation.
-2.375 + 2.375 + t = -9.792375861 + 2.375

Combine like terms: -2.375 + 2.375 = 0.000
0.000 + t = -9.792375861 + 2.375
t = -9.792375861 + 2.375

Combine like terms: -9.792375861 + 2.375 = -7.417375861
t = -7.417375861

Simplifying
t = -7.417375861


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {12.167375861, -7.417375861}
Solution
t = {12.167375861, -7.417375861}

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