0=-16t^2+15t+5

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Solution for 0=-16t^2+15t+5 equation:


Simplifying
0 = -16t2 + 15t + 5

Reorder the terms:
0 = 5 + 15t + -16t2

Solving
0 = 5 + 15t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -5 = -5
-5 + -15t + 16t2 = 5 + 15t + -16t2 + -5 + -15t + 16t2

Reorder the terms:
-5 + -15t + 16t2 = 5 + -5 + 15t + -15t + -16t2 + 16t2

Combine like terms: 5 + -5 = 0
-5 + -15t + 16t2 = 0 + 15t + -15t + -16t2 + 16t2
-5 + -15t + 16t2 = 15t + -15t + -16t2 + 16t2

Combine like terms: 15t + -15t = 0
-5 + -15t + 16t2 = 0 + -16t2 + 16t2
-5 + -15t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-5 + -15t + 16t2 = 0

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

Divide each side by '16'.
-0.3125 + -0.9375t + t2 = 0

Move the constant term to the right:

Add '0.3125' to each side of the equation.
-0.3125 + -0.9375t + 0.3125 + t2 = 0 + 0.3125

Reorder the terms:
-0.3125 + 0.3125 + -0.9375t + t2 = 0 + 0.3125

Combine like terms: -0.3125 + 0.3125 = 0.0000
0.0000 + -0.9375t + t2 = 0 + 0.3125
-0.9375t + t2 = 0 + 0.3125

Combine like terms: 0 + 0.3125 = 0.3125
-0.9375t + t2 = 0.3125

The t term is -0.9375t.  Take half its coefficient (-0.46875).
Square it (0.2197265625) and add it to both sides.

Add '0.2197265625' to each side of the equation.
-0.9375t + 0.2197265625 + t2 = 0.3125 + 0.2197265625

Reorder the terms:
0.2197265625 + -0.9375t + t2 = 0.3125 + 0.2197265625

Combine like terms: 0.3125 + 0.2197265625 = 0.5322265625
0.2197265625 + -0.9375t + t2 = 0.5322265625

Factor a perfect square on the left side:
(t + -0.46875)(t + -0.46875) = 0.5322265625

Calculate the square root of the right side: 0.729538596

Break this problem into two subproblems by setting 
(t + -0.46875) equal to 0.729538596 and -0.729538596.

Subproblem 1

t + -0.46875 = 0.729538596 Simplifying t + -0.46875 = 0.729538596 Reorder the terms: -0.46875 + t = 0.729538596 Solving -0.46875 + t = 0.729538596 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.46875' to each side of the equation. -0.46875 + 0.46875 + t = 0.729538596 + 0.46875 Combine like terms: -0.46875 + 0.46875 = 0.00000 0.00000 + t = 0.729538596 + 0.46875 t = 0.729538596 + 0.46875 Combine like terms: 0.729538596 + 0.46875 = 1.198288596 t = 1.198288596 Simplifying t = 1.198288596

Subproblem 2

t + -0.46875 = -0.729538596 Simplifying t + -0.46875 = -0.729538596 Reorder the terms: -0.46875 + t = -0.729538596 Solving -0.46875 + t = -0.729538596 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.46875' to each side of the equation. -0.46875 + 0.46875 + t = -0.729538596 + 0.46875 Combine like terms: -0.46875 + 0.46875 = 0.00000 0.00000 + t = -0.729538596 + 0.46875 t = -0.729538596 + 0.46875 Combine like terms: -0.729538596 + 0.46875 = -0.260788596 t = -0.260788596 Simplifying t = -0.260788596

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.198288596, -0.260788596}

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