0=-16t^2+3t+1.3

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Solution for 0=-16t^2+3t+1.3 equation:


Simplifying
0 = -16t2 + 3t + 1.3

Reorder the terms:
0 = 1.3 + 3t + -16t2

Solving
0 = 1.3 + 3t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -1.3 = -1.3
-1.3 + -3t + 16t2 = 1.3 + 3t + -16t2 + -1.3 + -3t + 16t2

Reorder the terms:
-1.3 + -3t + 16t2 = 1.3 + -1.3 + 3t + -3t + -16t2 + 16t2

Combine like terms: 1.3 + -1.3 = 0.0
-1.3 + -3t + 16t2 = 0.0 + 3t + -3t + -16t2 + 16t2
-1.3 + -3t + 16t2 = 3t + -3t + -16t2 + 16t2

Combine like terms: 3t + -3t = 0
-1.3 + -3t + 16t2 = 0 + -16t2 + 16t2
-1.3 + -3t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-1.3 + -3t + 16t2 = 0

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

Divide each side by '16'.
-0.08125 + -0.1875t + t2 = 0

Move the constant term to the right:

Add '0.08125' to each side of the equation.
-0.08125 + -0.1875t + 0.08125 + t2 = 0 + 0.08125

Reorder the terms:
-0.08125 + 0.08125 + -0.1875t + t2 = 0 + 0.08125

Combine like terms: -0.08125 + 0.08125 = 0.00000
0.00000 + -0.1875t + t2 = 0 + 0.08125
-0.1875t + t2 = 0 + 0.08125

Combine like terms: 0 + 0.08125 = 0.08125
-0.1875t + t2 = 0.08125

The t term is -0.1875t.  Take half its coefficient (-0.09375).
Square it (0.0087890625) and add it to both sides.

Add '0.0087890625' to each side of the equation.
-0.1875t + 0.0087890625 + t2 = 0.08125 + 0.0087890625

Reorder the terms:
0.0087890625 + -0.1875t + t2 = 0.08125 + 0.0087890625

Combine like terms: 0.08125 + 0.0087890625 = 0.0900390625
0.0087890625 + -0.1875t + t2 = 0.0900390625

Factor a perfect square on the left side:
(t + -0.09375)(t + -0.09375) = 0.0900390625

Calculate the square root of the right side: 0.300065097

Break this problem into two subproblems by setting 
(t + -0.09375) equal to 0.300065097 and -0.300065097.

Subproblem 1

t + -0.09375 = 0.300065097 Simplifying t + -0.09375 = 0.300065097 Reorder the terms: -0.09375 + t = 0.300065097 Solving -0.09375 + t = 0.300065097 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.09375' to each side of the equation. -0.09375 + 0.09375 + t = 0.300065097 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + t = 0.300065097 + 0.09375 t = 0.300065097 + 0.09375 Combine like terms: 0.300065097 + 0.09375 = 0.393815097 t = 0.393815097 Simplifying t = 0.393815097

Subproblem 2

t + -0.09375 = -0.300065097 Simplifying t + -0.09375 = -0.300065097 Reorder the terms: -0.09375 + t = -0.300065097 Solving -0.09375 + t = -0.300065097 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.09375' to each side of the equation. -0.09375 + 0.09375 + t = -0.300065097 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + t = -0.300065097 + 0.09375 t = -0.300065097 + 0.09375 Combine like terms: -0.300065097 + 0.09375 = -0.206315097 t = -0.206315097 Simplifying t = -0.206315097

Solution

The solution to the problem is based on the solutions from the subproblems. t = {0.393815097, -0.206315097}

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