t=1296-16t^2

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Solution for t=1296-16t^2 equation:


Simplifying
t = 1296 + -16t2

Solving
t = 1296 + -16t2

Solving for variable 't'.

Reorder the terms:
-1296 + t + 16t2 = 1296 + -16t2 + -1296 + 16t2

Reorder the terms:
-1296 + t + 16t2 = 1296 + -1296 + -16t2 + 16t2

Combine like terms: 1296 + -1296 = 0
-1296 + t + 16t2 = 0 + -16t2 + 16t2
-1296 + t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-1296 + t + 16t2 = 0

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

Divide each side by '16'.
-81 + 0.0625t + t2 = 0

Move the constant term to the right:

Add '81' to each side of the equation.
-81 + 0.0625t + 81 + t2 = 0 + 81

Reorder the terms:
-81 + 81 + 0.0625t + t2 = 0 + 81

Combine like terms: -81 + 81 = 0
0 + 0.0625t + t2 = 0 + 81
0.0625t + t2 = 0 + 81

Combine like terms: 0 + 81 = 81
0.0625t + t2 = 81

The t term is t.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.0625t + 0.25 + t2 = 81 + 0.25

Reorder the terms:
0.25 + 0.0625t + t2 = 81 + 0.25

Combine like terms: 81 + 0.25 = 81.25
0.25 + 0.0625t + t2 = 81.25

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = 81.25

Calculate the square root of the right side: 9.013878189

Break this problem into two subproblems by setting 
(t + 0.5) equal to 9.013878189 and -9.013878189.

Subproblem 1

t + 0.5 = 9.013878189 Simplifying t + 0.5 = 9.013878189 Reorder the terms: 0.5 + t = 9.013878189 Solving 0.5 + t = 9.013878189 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = 9.013878189 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 9.013878189 + -0.5 t = 9.013878189 + -0.5 Combine like terms: 9.013878189 + -0.5 = 8.513878189 t = 8.513878189 Simplifying t = 8.513878189

Subproblem 2

t + 0.5 = -9.013878189 Simplifying t + 0.5 = -9.013878189 Reorder the terms: 0.5 + t = -9.013878189 Solving 0.5 + t = -9.013878189 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = -9.013878189 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -9.013878189 + -0.5 t = -9.013878189 + -0.5 Combine like terms: -9.013878189 + -0.5 = -9.513878189 t = -9.513878189 Simplifying t = -9.513878189

Solution

The solution to the problem is based on the solutions from the subproblems. t = {8.513878189, -9.513878189}

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