0=-16t^2+36t+5

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Solution for 0=-16t^2+36t+5 equation:


Simplifying
0 = -16t2 + 36t + 5

Reorder the terms:
0 = 5 + 36t + -16t2

Solving
0 = 5 + 36t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -5 = -5
-5 + -36t + 16t2 = 5 + 36t + -16t2 + -5 + -36t + 16t2

Reorder the terms:
-5 + -36t + 16t2 = 5 + -5 + 36t + -36t + -16t2 + 16t2

Combine like terms: 5 + -5 = 0
-5 + -36t + 16t2 = 0 + 36t + -36t + -16t2 + 16t2
-5 + -36t + 16t2 = 36t + -36t + -16t2 + 16t2

Combine like terms: 36t + -36t = 0
-5 + -36t + 16t2 = 0 + -16t2 + 16t2
-5 + -36t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-5 + -36t + 16t2 = 0

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

Divide each side by '16'.
-0.3125 + -2.25t + t2 = 0

Move the constant term to the right:

Add '0.3125' to each side of the equation.
-0.3125 + -2.25t + 0.3125 + t2 = 0 + 0.3125

Reorder the terms:
-0.3125 + 0.3125 + -2.25t + t2 = 0 + 0.3125

Combine like terms: -0.3125 + 0.3125 = 0.0000
0.0000 + -2.25t + t2 = 0 + 0.3125
-2.25t + t2 = 0 + 0.3125

Combine like terms: 0 + 0.3125 = 0.3125
-2.25t + t2 = 0.3125

The t term is -2.25t.  Take half its coefficient (-1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
-2.25t + 1.265625 + t2 = 0.3125 + 1.265625

Reorder the terms:
1.265625 + -2.25t + t2 = 0.3125 + 1.265625

Combine like terms: 0.3125 + 1.265625 = 1.578125
1.265625 + -2.25t + t2 = 1.578125

Factor a perfect square on the left side:
(t + -1.125)(t + -1.125) = 1.578125

Calculate the square root of the right side: 1.256234453

Break this problem into two subproblems by setting 
(t + -1.125) equal to 1.256234453 and -1.256234453.

Subproblem 1

t + -1.125 = 1.256234453 Simplifying t + -1.125 = 1.256234453 Reorder the terms: -1.125 + t = 1.256234453 Solving -1.125 + t = 1.256234453 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + t = 1.256234453 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + t = 1.256234453 + 1.125 t = 1.256234453 + 1.125 Combine like terms: 1.256234453 + 1.125 = 2.381234453 t = 2.381234453 Simplifying t = 2.381234453

Subproblem 2

t + -1.125 = -1.256234453 Simplifying t + -1.125 = -1.256234453 Reorder the terms: -1.125 + t = -1.256234453 Solving -1.125 + t = -1.256234453 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + t = -1.256234453 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + t = -1.256234453 + 1.125 t = -1.256234453 + 1.125 Combine like terms: -1.256234453 + 1.125 = -0.131234453 t = -0.131234453 Simplifying t = -0.131234453

Solution

The solution to the problem is based on the solutions from the subproblems. t = {2.381234453, -0.131234453}

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