0=-16t^2+96t+3

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Solution for 0=-16t^2+96t+3 equation:


Simplifying
0 = -16t2 + 96t + 3

Reorder the terms:
0 = 3 + 96t + -16t2

Solving
0 = 3 + 96t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -3 = -3
-3 + -96t + 16t2 = 3 + 96t + -16t2 + -3 + -96t + 16t2

Reorder the terms:
-3 + -96t + 16t2 = 3 + -3 + 96t + -96t + -16t2 + 16t2

Combine like terms: 3 + -3 = 0
-3 + -96t + 16t2 = 0 + 96t + -96t + -16t2 + 16t2
-3 + -96t + 16t2 = 96t + -96t + -16t2 + 16t2

Combine like terms: 96t + -96t = 0
-3 + -96t + 16t2 = 0 + -16t2 + 16t2
-3 + -96t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-3 + -96t + 16t2 = 0

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

Divide each side by '16'.
-0.1875 + -6t + t2 = 0

Move the constant term to the right:

Add '0.1875' to each side of the equation.
-0.1875 + -6t + 0.1875 + t2 = 0 + 0.1875

Reorder the terms:
-0.1875 + 0.1875 + -6t + t2 = 0 + 0.1875

Combine like terms: -0.1875 + 0.1875 = 0.0000
0.0000 + -6t + t2 = 0 + 0.1875
-6t + t2 = 0 + 0.1875

Combine like terms: 0 + 0.1875 = 0.1875
-6t + t2 = 0.1875

The t term is -6t.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6t + 9 + t2 = 0.1875 + 9

Reorder the terms:
9 + -6t + t2 = 0.1875 + 9

Combine like terms: 0.1875 + 9 = 9.1875
9 + -6t + t2 = 9.1875

Factor a perfect square on the left side:
(t + -3)(t + -3) = 9.1875

Calculate the square root of the right side: 3.031088913

Break this problem into two subproblems by setting 
(t + -3) equal to 3.031088913 and -3.031088913.

Subproblem 1

t + -3 = 3.031088913 Simplifying t + -3 = 3.031088913 Reorder the terms: -3 + t = 3.031088913 Solving -3 + t = 3.031088913 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = 3.031088913 + 3 Combine like terms: -3 + 3 = 0 0 + t = 3.031088913 + 3 t = 3.031088913 + 3 Combine like terms: 3.031088913 + 3 = 6.031088913 t = 6.031088913 Simplifying t = 6.031088913

Subproblem 2

t + -3 = -3.031088913 Simplifying t + -3 = -3.031088913 Reorder the terms: -3 + t = -3.031088913 Solving -3 + t = -3.031088913 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = -3.031088913 + 3 Combine like terms: -3 + 3 = 0 0 + t = -3.031088913 + 3 t = -3.031088913 + 3 Combine like terms: -3.031088913 + 3 = -0.031088913 t = -0.031088913 Simplifying t = -0.031088913

Solution

The solution to the problem is based on the solutions from the subproblems. t = {6.031088913, -0.031088913}

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