60=16t^2+60t-2

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Solution for 60=16t^2+60t-2 equation: 


Simplifying
60 = 16t2 + 60t + -2

Reorder the terms:
60 = -2 + 60t + 16t2

Solving
60 = -2 + 60t + 16t2

Solving for variable 't'.

Combine like terms: 60 + 2 = 62
62 + -60t + -16t2 = -2 + 60t + 16t2 + 2 + -60t + -16t2

Reorder the terms:
62 + -60t + -16t2 = -2 + 2 + 60t + -60t + 16t2 + -16t2

Combine like terms: -2 + 2 = 0
62 + -60t + -16t2 = 0 + 60t + -60t + 16t2 + -16t2
62 + -60t + -16t2 = 60t + -60t + 16t2 + -16t2

Combine like terms: 60t + -60t = 0
62 + -60t + -16t2 = 0 + 16t2 + -16t2
62 + -60t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
62 + -60t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(31 + -30t + -8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(31 + -30t + -8t2)' equal to zero and attempt to solve:

Simplifying
31 + -30t + -8t2 = 0

Solving
31 + -30t + -8t2 = 0

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

Divide each side by '-8'.
-3.875 + 3.75t + t2 = 0

Move the constant term to the right:

Add '3.875' to each side of the equation.
-3.875 + 3.75t + 3.875 + t2 = 0 + 3.875

Reorder the terms:
-3.875 + 3.875 + 3.75t + t2 = 0 + 3.875

Combine like terms: -3.875 + 3.875 = 0.000
0.000 + 3.75t + t2 = 0 + 3.875
3.75t + t2 = 0 + 3.875

Combine like terms: 0 + 3.875 = 3.875
3.75t + t2 = 3.875

The t term is 3.75t.  Take half its coefficient (1.875).
Square it (3.515625) and add it to both sides.

Add '3.515625' to each side of the equation.
3.75t + 3.515625 + t2 = 3.875 + 3.515625

Reorder the terms:
3.515625 + 3.75t + t2 = 3.875 + 3.515625

Combine like terms: 3.875 + 3.515625 = 7.390625
3.515625 + 3.75t + t2 = 7.390625

Factor a perfect square on the left side:
(t + 1.875)(t + 1.875) = 7.390625

Calculate the square root of the right side: 2.718570396

Break this problem into two subproblems by setting 
(t + 1.875) equal to 2.718570396 and -2.718570396.


Subproblem 1
t + 1.875 = 2.718570396

Simplifying
t + 1.875 = 2.718570396

Reorder the terms:
1.875 + t = 2.718570396

Solving
1.875 + t = 2.718570396

Solving for variable 't'.

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

Add '-1.875' to each side of the equation.
1.875 + -1.875 + t = 2.718570396 + -1.875

Combine like terms: 1.875 + -1.875 = 0.000
0.000 + t = 2.718570396 + -1.875
t = 2.718570396 + -1.875

Combine like terms: 2.718570396 + -1.875 = 0.843570396
t = 0.843570396

Simplifying
t = 0.843570396


Subproblem 2
t + 1.875 = -2.718570396

Simplifying
t + 1.875 = -2.718570396

Reorder the terms:
1.875 + t = -2.718570396

Solving
1.875 + t = -2.718570396

Solving for variable 't'.

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

Add '-1.875' to each side of the equation.
1.875 + -1.875 + t = -2.718570396 + -1.875

Combine like terms: 1.875 + -1.875 = 0.000
0.000 + t = -2.718570396 + -1.875
t = -2.718570396 + -1.875

Combine like terms: -2.718570396 + -1.875 = -4.593570396
t = -4.593570396

Simplifying
t = -4.593570396


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.843570396, -4.593570396}
Solution
t = {0.843570396, -4.593570396}

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