-16t^2+24t+1300=0

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Solution for -16t^2+24t+1300=0 equation: 


Simplifying
-16t2 + 24t + 1300 = 0

Reorder the terms:
1300 + 24t + -16t2 = 0

Solving
1300 + 24t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(325 + 6t + -4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(325 + 6t + -4t2)' equal to zero and attempt to solve:

Simplifying
325 + 6t + -4t2 = 0

Solving
325 + 6t + -4t2 = 0

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

Divide each side by '-4'.
-81.25 + -1.5t + t2 = 0

Move the constant term to the right:

Add '81.25' to each side of the equation.
-81.25 + -1.5t + 81.25 + t2 = 0 + 81.25

Reorder the terms:
-81.25 + 81.25 + -1.5t + t2 = 0 + 81.25

Combine like terms: -81.25 + 81.25 = 0.00
0.00 + -1.5t + t2 = 0 + 81.25
-1.5t + t2 = 0 + 81.25

Combine like terms: 0 + 81.25 = 81.25
-1.5t + t2 = 81.25

The t term is -1.5t.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5t + 0.5625 + t2 = 81.25 + 0.5625

Reorder the terms:
0.5625 + -1.5t + t2 = 81.25 + 0.5625

Combine like terms: 81.25 + 0.5625 = 81.8125
0.5625 + -1.5t + t2 = 81.8125

Factor a perfect square on the left side:
(t + -0.75)(t + -0.75) = 81.8125

Calculate the square root of the right side: 9.045026258

Break this problem into two subproblems by setting 
(t + -0.75) equal to 9.045026258 and -9.045026258.


Subproblem 1
t + -0.75 = 9.045026258

Simplifying
t + -0.75 = 9.045026258

Reorder the terms:
-0.75 + t = 9.045026258

Solving
-0.75 + t = 9.045026258

Solving for variable 't'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + t = 9.045026258 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + t = 9.045026258 + 0.75
t = 9.045026258 + 0.75

Combine like terms: 9.045026258 + 0.75 = 9.795026258
t = 9.795026258

Simplifying
t = 9.795026258


Subproblem 2
t + -0.75 = -9.045026258

Simplifying
t + -0.75 = -9.045026258

Reorder the terms:
-0.75 + t = -9.045026258

Solving
-0.75 + t = -9.045026258

Solving for variable 't'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + t = -9.045026258 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + t = -9.045026258 + 0.75
t = -9.045026258 + 0.75

Combine like terms: -9.045026258 + 0.75 = -8.295026258
t = -8.295026258

Simplifying
t = -8.295026258


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {9.795026258, -8.295026258}
Solution
t = {9.795026258, -8.295026258}

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