-16t^2+76t+46=0

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Solution for -16t^2+76t+46=0 equation: 


Simplifying
-16t2 + 76t + 46 = 0

Reorder the terms:
46 + 76t + -16t2 = 0

Solving
46 + 76t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(23 + 38t + -8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(23 + 38t + -8t2)' equal to zero and attempt to solve:

Simplifying
23 + 38t + -8t2 = 0

Solving
23 + 38t + -8t2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-2.875 + -4.75t + t2 = 0

Move the constant term to the right:

Add '2.875' to each side of the equation.
-2.875 + -4.75t + 2.875 + t2 = 0 + 2.875

Reorder the terms:
-2.875 + 2.875 + -4.75t + t2 = 0 + 2.875

Combine like terms: -2.875 + 2.875 = 0.000
0.000 + -4.75t + t2 = 0 + 2.875
-4.75t + t2 = 0 + 2.875

Combine like terms: 0 + 2.875 = 2.875
-4.75t + t2 = 2.875

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 = 2.875 + 5.640625

Reorder the terms:
5.640625 + -4.75t + t2 = 2.875 + 5.640625

Combine like terms: 2.875 + 5.640625 = 8.515625
5.640625 + -4.75t + t2 = 8.515625

Factor a perfect square on the left side:
(t + -2.375)(t + -2.375) = 8.515625

Calculate the square root of the right side: 2.918154382

Break this problem into two subproblems by setting 
(t + -2.375) equal to 2.918154382 and -2.918154382.


Subproblem 1
t + -2.375 = 2.918154382

Simplifying
t + -2.375 = 2.918154382

Reorder the terms:
-2.375 + t = 2.918154382

Solving
-2.375 + t = 2.918154382

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 = 2.918154382 + 2.375

Combine like terms: -2.375 + 2.375 = 0.000
0.000 + t = 2.918154382 + 2.375
t = 2.918154382 + 2.375

Combine like terms: 2.918154382 + 2.375 = 5.293154382
t = 5.293154382

Simplifying
t = 5.293154382


Subproblem 2
t + -2.375 = -2.918154382

Simplifying
t + -2.375 = -2.918154382

Reorder the terms:
-2.375 + t = -2.918154382

Solving
-2.375 + t = -2.918154382

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 = -2.918154382 + 2.375

Combine like terms: -2.375 + 2.375 = 0.000
0.000 + t = -2.918154382 + 2.375
t = -2.918154382 + 2.375

Combine like terms: -2.918154382 + 2.375 = -0.543154382
t = -0.543154382

Simplifying
t = -0.543154382


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {5.293154382, -0.543154382}
Solution
t = {5.293154382, -0.543154382}

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