-16t^2+14t+350=0

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Solution for -16t^2+14t+350=0 equation: 


Simplifying
-16t2 + 14t + 350 = 0

Reorder the terms:
350 + 14t + -16t2 = 0

Solving
350 + 14t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(175 + 7t + -8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(175 + 7t + -8t2)' equal to zero and attempt to solve:

Simplifying
175 + 7t + -8t2 = 0

Solving
175 + 7t + -8t2 = 0

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

Divide each side by '-8'.
-21.875 + -0.875t + t2 = 0

Move the constant term to the right:

Add '21.875' to each side of the equation.
-21.875 + -0.875t + 21.875 + t2 = 0 + 21.875

Reorder the terms:
-21.875 + 21.875 + -0.875t + t2 = 0 + 21.875

Combine like terms: -21.875 + 21.875 = 0.000
0.000 + -0.875t + t2 = 0 + 21.875
-0.875t + t2 = 0 + 21.875

Combine like terms: 0 + 21.875 = 21.875
-0.875t + t2 = 21.875

The t term is -0.875t.  Take half its coefficient (-0.4375).
Square it (0.19140625) and add it to both sides.

Add '0.19140625' to each side of the equation.
-0.875t + 0.19140625 + t2 = 21.875 + 0.19140625

Reorder the terms:
0.19140625 + -0.875t + t2 = 21.875 + 0.19140625

Combine like terms: 21.875 + 0.19140625 = 22.06640625
0.19140625 + -0.875t + t2 = 22.06640625

Factor a perfect square on the left side:
(t + -0.4375)(t + -0.4375) = 22.06640625

Calculate the square root of the right side: 4.697489356

Break this problem into two subproblems by setting 
(t + -0.4375) equal to 4.697489356 and -4.697489356.


Subproblem 1
t + -0.4375 = 4.697489356

Simplifying
t + -0.4375 = 4.697489356

Reorder the terms:
-0.4375 + t = 4.697489356

Solving
-0.4375 + t = 4.697489356

Solving for variable 't'.

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

Add '0.4375' to each side of the equation.
-0.4375 + 0.4375 + t = 4.697489356 + 0.4375

Combine like terms: -0.4375 + 0.4375 = 0.0000
0.0000 + t = 4.697489356 + 0.4375
t = 4.697489356 + 0.4375

Combine like terms: 4.697489356 + 0.4375 = 5.134989356
t = 5.134989356

Simplifying
t = 5.134989356


Subproblem 2
t + -0.4375 = -4.697489356

Simplifying
t + -0.4375 = -4.697489356

Reorder the terms:
-0.4375 + t = -4.697489356

Solving
-0.4375 + t = -4.697489356

Solving for variable 't'.

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

Add '0.4375' to each side of the equation.
-0.4375 + 0.4375 + t = -4.697489356 + 0.4375

Combine like terms: -0.4375 + 0.4375 = 0.0000
0.0000 + t = -4.697489356 + 0.4375
t = -4.697489356 + 0.4375

Combine like terms: -4.697489356 + 0.4375 = -4.259989356
t = -4.259989356

Simplifying
t = -4.259989356


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {5.134989356, -4.259989356}
Solution
t = {5.134989356, -4.259989356}

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