16t^2-215t+97=0

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Solution for 16t^2-215t+97=0 equation: 


Simplifying
16t2 + -215t + 97 = 0

Reorder the terms:
97 + -215t + 16t2 = 0

Solving
97 + -215t + 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'.
6.0625 + -13.4375t + t2 = 0

Move the constant term to the right:

Add '-6.0625' to each side of the equation.
6.0625 + -13.4375t + -6.0625 + t2 = 0 + -6.0625

Reorder the terms:
6.0625 + -6.0625 + -13.4375t + t2 = 0 + -6.0625

Combine like terms: 6.0625 + -6.0625 = 0.0000
0.0000 + -13.4375t + t2 = 0 + -6.0625
-13.4375t + t2 = 0 + -6.0625

Combine like terms: 0 + -6.0625 = -6.0625
-13.4375t + t2 = -6.0625

The t term is -13.4375t.  Take half its coefficient (-6.71875).
Square it (45.14160156) and add it to both sides.

Add '45.14160156' to each side of the equation.
-13.4375t + 45.14160156 + t2 = -6.0625 + 45.14160156

Reorder the terms:
45.14160156 + -13.4375t + t2 = -6.0625 + 45.14160156

Combine like terms: -6.0625 + 45.14160156 = 39.07910156
45.14160156 + -13.4375t + t2 = 39.07910156

Factor a perfect square on the left side:
(t + -6.71875)(t + -6.71875) = 39.07910156

Calculate the square root of the right side: 6.251327984

Break this problem into two subproblems by setting 
(t + -6.71875) equal to 6.251327984 and -6.251327984.


Subproblem 1
t + -6.71875 = 6.251327984

Simplifying
t + -6.71875 = 6.251327984

Reorder the terms:
-6.71875 + t = 6.251327984

Solving
-6.71875 + t = 6.251327984

Solving for variable 't'.

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

Add '6.71875' to each side of the equation.
-6.71875 + 6.71875 + t = 6.251327984 + 6.71875

Combine like terms: -6.71875 + 6.71875 = 0.00000
0.00000 + t = 6.251327984 + 6.71875
t = 6.251327984 + 6.71875

Combine like terms: 6.251327984 + 6.71875 = 12.970077984
t = 12.970077984

Simplifying
t = 12.970077984


Subproblem 2
t + -6.71875 = -6.251327984

Simplifying
t + -6.71875 = -6.251327984

Reorder the terms:
-6.71875 + t = -6.251327984

Solving
-6.71875 + t = -6.251327984

Solving for variable 't'.

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

Add '6.71875' to each side of the equation.
-6.71875 + 6.71875 + t = -6.251327984 + 6.71875

Combine like terms: -6.71875 + 6.71875 = 0.00000
0.00000 + t = -6.251327984 + 6.71875
t = -6.251327984 + 6.71875

Combine like terms: -6.251327984 + 6.71875 = 0.467422016
t = 0.467422016

Simplifying
t = 0.467422016


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {12.970077984, 0.467422016}

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