20=-16t^2+96t+7

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Solution for 20=-16t^2+96t+7 equation:


Simplifying
20 = -16t2 + 96t + 7

Reorder the terms:
20 = 7 + 96t + -16t2

Solving
20 = 7 + 96t + -16t2

Solving for variable 't'.

Combine like terms: 20 + -7 = 13
13 + -96t + 16t2 = 7 + 96t + -16t2 + -7 + -96t + 16t2

Reorder the terms:
13 + -96t + 16t2 = 7 + -7 + 96t + -96t + -16t2 + 16t2

Combine like terms: 7 + -7 = 0
13 + -96t + 16t2 = 0 + 96t + -96t + -16t2 + 16t2
13 + -96t + 16t2 = 96t + -96t + -16t2 + 16t2

Combine like terms: 96t + -96t = 0
13 + -96t + 16t2 = 0 + -16t2 + 16t2
13 + -96t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
13 + -96t + 16t2 = 0

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

Divide each side by '16'.
0.8125 + -6t + t2 = 0

Move the constant term to the right:

Add '-0.8125' to each side of the equation.
0.8125 + -6t + -0.8125 + t2 = 0 + -0.8125

Reorder the terms:
0.8125 + -0.8125 + -6t + t2 = 0 + -0.8125

Combine like terms: 0.8125 + -0.8125 = 0.0000
0.0000 + -6t + t2 = 0 + -0.8125
-6t + t2 = 0 + -0.8125

Combine like terms: 0 + -0.8125 = -0.8125
-6t + t2 = -0.8125

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 = -0.8125 + 9

Reorder the terms:
9 + -6t + t2 = -0.8125 + 9

Combine like terms: -0.8125 + 9 = 8.1875
9 + -6t + t2 = 8.1875

Factor a perfect square on the left side:
(t + -3)(t + -3) = 8.1875

Calculate the square root of the right side: 2.861380786

Break this problem into two subproblems by setting 
(t + -3) equal to 2.861380786 and -2.861380786.

Subproblem 1

t + -3 = 2.861380786 Simplifying t + -3 = 2.861380786 Reorder the terms: -3 + t = 2.861380786 Solving -3 + t = 2.861380786 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 = 2.861380786 + 3 Combine like terms: -3 + 3 = 0 0 + t = 2.861380786 + 3 t = 2.861380786 + 3 Combine like terms: 2.861380786 + 3 = 5.861380786 t = 5.861380786 Simplifying t = 5.861380786

Subproblem 2

t + -3 = -2.861380786 Simplifying t + -3 = -2.861380786 Reorder the terms: -3 + t = -2.861380786 Solving -3 + t = -2.861380786 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 = -2.861380786 + 3 Combine like terms: -3 + 3 = 0 0 + t = -2.861380786 + 3 t = -2.861380786 + 3 Combine like terms: -2.861380786 + 3 = 0.138619214 t = 0.138619214 Simplifying t = 0.138619214

Solution

The solution to the problem is based on the solutions from the subproblems. t = {5.861380786, 0.138619214}

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