-16t^2+80t+3=0

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Solution for -16t^2+80t+3=0 equation:


Simplifying
-16t2 + 80t + 3 = 0

Reorder the terms:
3 + 80t + -16t2 = 0

Solving
3 + 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'.
-0.1875 + -5t + t2 = 0

Move the constant term to the right:

Add '0.1875' to each side of the equation.
-0.1875 + -5t + 0.1875 + t2 = 0 + 0.1875

Reorder the terms:
-0.1875 + 0.1875 + -5t + t2 = 0 + 0.1875

Combine like terms: -0.1875 + 0.1875 = 0.0000
0.0000 + -5t + t2 = 0 + 0.1875
-5t + t2 = 0 + 0.1875

Combine like terms: 0 + 0.1875 = 0.1875
-5t + t2 = 0.1875

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 = 0.1875 + 6.25

Reorder the terms:
6.25 + -5t + t2 = 0.1875 + 6.25

Combine like terms: 0.1875 + 6.25 = 6.4375
6.25 + -5t + t2 = 6.4375

Factor a perfect square on the left side:
(t + -2.5)(t + -2.5) = 6.4375

Calculate the square root of the right side: 2.537222891

Break this problem into two subproblems by setting 
(t + -2.5) equal to 2.537222891 and -2.537222891.

Subproblem 1

t + -2.5 = 2.537222891 Simplifying t + -2.5 = 2.537222891 Reorder the terms: -2.5 + t = 2.537222891 Solving -2.5 + t = 2.537222891 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 = 2.537222891 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = 2.537222891 + 2.5 t = 2.537222891 + 2.5 Combine like terms: 2.537222891 + 2.5 = 5.037222891 t = 5.037222891 Simplifying t = 5.037222891

Subproblem 2

t + -2.5 = -2.537222891 Simplifying t + -2.5 = -2.537222891 Reorder the terms: -2.5 + t = -2.537222891 Solving -2.5 + t = -2.537222891 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 = -2.537222891 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = -2.537222891 + 2.5 t = -2.537222891 + 2.5 Combine like terms: -2.537222891 + 2.5 = -0.037222891 t = -0.037222891 Simplifying t = -0.037222891

Solution

The solution to the problem is based on the solutions from the subproblems. t = {5.037222891, -0.037222891}

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