93=201t-16t^2

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Solution for 93=201t-16t^2 equation:


Simplifying
93 = 201t + -16t2

Solving
93 = 201t + -16t2

Solving for variable 't'.

Reorder the terms:
93 + -201t + 16t2 = 201t + -201t + -16t2 + 16t2

Combine like terms: 201t + -201t = 0
93 + -201t + 16t2 = 0 + -16t2 + 16t2
93 + -201t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
93 + -201t + 16t2 = 0

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

Divide each side by '16'.
5.8125 + -12.5625t + t2 = 0

Move the constant term to the right:

Add '-5.8125' to each side of the equation.
5.8125 + -12.5625t + -5.8125 + t2 = 0 + -5.8125

Reorder the terms:
5.8125 + -5.8125 + -12.5625t + t2 = 0 + -5.8125

Combine like terms: 5.8125 + -5.8125 = 0.0000
0.0000 + -12.5625t + t2 = 0 + -5.8125
-12.5625t + t2 = 0 + -5.8125

Combine like terms: 0 + -5.8125 = -5.8125
-12.5625t + t2 = -5.8125

The t term is -12.5625t.  Take half its coefficient (-6.28125).
Square it (39.45410156) and add it to both sides.

Add '39.45410156' to each side of the equation.
-12.5625t + 39.45410156 + t2 = -5.8125 + 39.45410156

Reorder the terms:
39.45410156 + -12.5625t + t2 = -5.8125 + 39.45410156

Combine like terms: -5.8125 + 39.45410156 = 33.64160156
39.45410156 + -12.5625t + t2 = 33.64160156

Factor a perfect square on the left side:
(t + -6.28125)(t + -6.28125) = 33.64160156

Calculate the square root of the right side: 5.800138064

Break this problem into two subproblems by setting 
(t + -6.28125) equal to 5.800138064 and -5.800138064.

Subproblem 1

t + -6.28125 = 5.800138064 Simplifying t + -6.28125 = 5.800138064 Reorder the terms: -6.28125 + t = 5.800138064 Solving -6.28125 + t = 5.800138064 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.28125' to each side of the equation. -6.28125 + 6.28125 + t = 5.800138064 + 6.28125 Combine like terms: -6.28125 + 6.28125 = 0.00000 0.00000 + t = 5.800138064 + 6.28125 t = 5.800138064 + 6.28125 Combine like terms: 5.800138064 + 6.28125 = 12.081388064 t = 12.081388064 Simplifying t = 12.081388064

Subproblem 2

t + -6.28125 = -5.800138064 Simplifying t + -6.28125 = -5.800138064 Reorder the terms: -6.28125 + t = -5.800138064 Solving -6.28125 + t = -5.800138064 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.28125' to each side of the equation. -6.28125 + 6.28125 + t = -5.800138064 + 6.28125 Combine like terms: -6.28125 + 6.28125 = 0.00000 0.00000 + t = -5.800138064 + 6.28125 t = -5.800138064 + 6.28125 Combine like terms: -5.800138064 + 6.28125 = 0.481111936 t = 0.481111936 Simplifying t = 0.481111936

Solution

The solution to the problem is based on the solutions from the subproblems. t = {12.081388064, 0.481111936}

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