80t-16t^2+3.5=0

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Solution for 80t-16t^2+3.5=0 equation: 


Simplifying
80t + -16t2 + 3.5 = 0

Reorder the terms:
3.5 + 80t + -16t2 = 0

Solving
3.5 + 80t + -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'.
-0.21875 + -5t + t2 = 0

Move the constant term to the right:

Add '0.21875' to each side of the equation.
-0.21875 + -5t + 0.21875 + t2 = 0 + 0.21875

Reorder the terms:
-0.21875 + 0.21875 + -5t + t2 = 0 + 0.21875

Combine like terms: -0.21875 + 0.21875 = 0.00000
0.00000 + -5t + t2 = 0 + 0.21875
-5t + t2 = 0 + 0.21875

Combine like terms: 0 + 0.21875 = 0.21875
-5t + t2 = 0.21875

The t term is -5t.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5t + 6.25 + t2 = 0.21875 + 6.25

Reorder the terms:
6.25 + -5t + t2 = 0.21875 + 6.25

Combine like terms: 0.21875 + 6.25 = 6.46875
6.25 + -5t + t2 = 6.46875

Factor a perfect square on the left side:
(t + -2.5)(t + -2.5) = 6.46875

Calculate the square root of the right side: 2.543373744

Break this problem into two subproblems by setting 
(t + -2.5) equal to 2.543373744 and -2.543373744.


Subproblem 1
t + -2.5 = 2.543373744

Simplifying
t + -2.5 = 2.543373744

Reorder the terms:
-2.5 + t = 2.543373744

Solving
-2.5 + t = 2.543373744

Solving for variable 't'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + t = 2.543373744 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = 2.543373744 + 2.5
t = 2.543373744 + 2.5

Combine like terms: 2.543373744 + 2.5 = 5.043373744
t = 5.043373744

Simplifying
t = 5.043373744


Subproblem 2
t + -2.5 = -2.543373744

Simplifying
t + -2.5 = -2.543373744

Reorder the terms:
-2.5 + t = -2.543373744

Solving
-2.5 + t = -2.543373744

Solving for variable 't'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + t = -2.543373744 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = -2.543373744 + 2.5
t = -2.543373744 + 2.5

Combine like terms: -2.543373744 + 2.5 = -0.043373744
t = -0.043373744

Simplifying
t = -0.043373744


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {5.043373744, -0.043373744}

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