16t^2-102t-455=0

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Solution for 16t^2-102t-455=0 equation:


Simplifying
16t2 + -102t + -455 = 0

Reorder the terms:
-455 + -102t + 16t2 = 0

Solving
-455 + -102t + 16t2 = 0

Solving for variable 't'.

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

Divide each side by '16'.
-28.4375 + -6.375t + t2 = 0

Move the constant term to the right:

Add '28.4375' to each side of the equation.
-28.4375 + -6.375t + 28.4375 + t2 = 0 + 28.4375

Reorder the terms:
-28.4375 + 28.4375 + -6.375t + t2 = 0 + 28.4375

Combine like terms: -28.4375 + 28.4375 = 0.0000
0.0000 + -6.375t + t2 = 0 + 28.4375
-6.375t + t2 = 0 + 28.4375

Combine like terms: 0 + 28.4375 = 28.4375
-6.375t + t2 = 28.4375

The t term is -6.375t.  Take half its coefficient (-3.1875).
Square it (10.16015625) and add it to both sides.

Add '10.16015625' to each side of the equation.
-6.375t + 10.16015625 + t2 = 28.4375 + 10.16015625

Reorder the terms:
10.16015625 + -6.375t + t2 = 28.4375 + 10.16015625

Combine like terms: 28.4375 + 10.16015625 = 38.59765625
10.16015625 + -6.375t + t2 = 38.59765625

Factor a perfect square on the left side:
(t + -3.1875)(t + -3.1875) = 38.59765625

Calculate the square root of the right side: 6.212701204

Break this problem into two subproblems by setting 
(t + -3.1875) equal to 6.212701204 and -6.212701204.

Subproblem 1

t + -3.1875 = 6.212701204 Simplifying t + -3.1875 = 6.212701204 Reorder the terms: -3.1875 + t = 6.212701204 Solving -3.1875 + t = 6.212701204 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.1875' to each side of the equation. -3.1875 + 3.1875 + t = 6.212701204 + 3.1875 Combine like terms: -3.1875 + 3.1875 = 0.0000 0.0000 + t = 6.212701204 + 3.1875 t = 6.212701204 + 3.1875 Combine like terms: 6.212701204 + 3.1875 = 9.400201204 t = 9.400201204 Simplifying t = 9.400201204

Subproblem 2

t + -3.1875 = -6.212701204 Simplifying t + -3.1875 = -6.212701204 Reorder the terms: -3.1875 + t = -6.212701204 Solving -3.1875 + t = -6.212701204 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.1875' to each side of the equation. -3.1875 + 3.1875 + t = -6.212701204 + 3.1875 Combine like terms: -3.1875 + 3.1875 = 0.0000 0.0000 + t = -6.212701204 + 3.1875 t = -6.212701204 + 3.1875 Combine like terms: -6.212701204 + 3.1875 = -3.025201204 t = -3.025201204 Simplifying t = -3.025201204

Solution

The solution to the problem is based on the solutions from the subproblems. t = {9.400201204, -3.025201204}

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