5=-16t^2+64t+0

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Solution for 5=-16t^2+64t+0 equation:


Simplifying
5 = -16t2 + 64t + 0

Reorder the terms:
5 = 0 + 64t + -16t2
Remove the zero:
5 = 64t + -16t2

Solving
5 = 64t + -16t2

Solving for variable 't'.

Reorder the terms:
5 + -64t + 16t2 = 64t + -64t + -16t2 + 16t2

Combine like terms: 64t + -64t = 0
5 + -64t + 16t2 = 0 + -16t2 + 16t2
5 + -64t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
5 + -64t + 16t2 = 0

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

Divide each side by '16'.
0.3125 + -4t + t2 = 0

Move the constant term to the right:

Add '-0.3125' to each side of the equation.
0.3125 + -4t + -0.3125 + t2 = 0 + -0.3125

Reorder the terms:
0.3125 + -0.3125 + -4t + t2 = 0 + -0.3125

Combine like terms: 0.3125 + -0.3125 = 0.0000
0.0000 + -4t + t2 = 0 + -0.3125
-4t + t2 = 0 + -0.3125

Combine like terms: 0 + -0.3125 = -0.3125
-4t + t2 = -0.3125

The t term is -4t.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4t + 4 + t2 = -0.3125 + 4

Reorder the terms:
4 + -4t + t2 = -0.3125 + 4

Combine like terms: -0.3125 + 4 = 3.6875
4 + -4t + t2 = 3.6875

Factor a perfect square on the left side:
(t + -2)(t + -2) = 3.6875

Calculate the square root of the right side: 1.920286437

Break this problem into two subproblems by setting 
(t + -2) equal to 1.920286437 and -1.920286437.

Subproblem 1

t + -2 = 1.920286437 Simplifying t + -2 = 1.920286437 Reorder the terms: -2 + t = 1.920286437 Solving -2 + t = 1.920286437 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 1.920286437 + 2 Combine like terms: -2 + 2 = 0 0 + t = 1.920286437 + 2 t = 1.920286437 + 2 Combine like terms: 1.920286437 + 2 = 3.920286437 t = 3.920286437 Simplifying t = 3.920286437

Subproblem 2

t + -2 = -1.920286437 Simplifying t + -2 = -1.920286437 Reorder the terms: -2 + t = -1.920286437 Solving -2 + t = -1.920286437 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -1.920286437 + 2 Combine like terms: -2 + 2 = 0 0 + t = -1.920286437 + 2 t = -1.920286437 + 2 Combine like terms: -1.920286437 + 2 = 0.079713563 t = 0.079713563 Simplifying t = 0.079713563

Solution

The solution to the problem is based on the solutions from the subproblems. t = {3.920286437, 0.079713563}

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