0=-16t^2+15t+8

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Solution for 0=-16t^2+15t+8 equation:


Simplifying
0 = -16t2 + 15t + 8

Reorder the terms:
0 = 8 + 15t + -16t2

Solving
0 = 8 + 15t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -8 = -8
-8 + -15t + 16t2 = 8 + 15t + -16t2 + -8 + -15t + 16t2

Reorder the terms:
-8 + -15t + 16t2 = 8 + -8 + 15t + -15t + -16t2 + 16t2

Combine like terms: 8 + -8 = 0
-8 + -15t + 16t2 = 0 + 15t + -15t + -16t2 + 16t2
-8 + -15t + 16t2 = 15t + -15t + -16t2 + 16t2

Combine like terms: 15t + -15t = 0
-8 + -15t + 16t2 = 0 + -16t2 + 16t2
-8 + -15t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-8 + -15t + 16t2 = 0

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

Divide each side by '16'.
-0.5 + -0.9375t + t2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -0.9375t + 0.5 + t2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -0.9375t + t2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -0.9375t + t2 = 0 + 0.5
-0.9375t + t2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-0.9375t + t2 = 0.5

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 = 0.5 + 0.2197265625

Reorder the terms:
0.2197265625 + -0.9375t + t2 = 0.5 + 0.2197265625

Combine like terms: 0.5 + 0.2197265625 = 0.7197265625
0.2197265625 + -0.9375t + t2 = 0.7197265625

Factor a perfect square on the left side:
(t + -0.46875)(t + -0.46875) = 0.7197265625

Calculate the square root of the right side: 0.848366998

Break this problem into two subproblems by setting 
(t + -0.46875) equal to 0.848366998 and -0.848366998.

Subproblem 1

t + -0.46875 = 0.848366998 Simplifying t + -0.46875 = 0.848366998 Reorder the terms: -0.46875 + t = 0.848366998 Solving -0.46875 + t = 0.848366998 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 = 0.848366998 + 0.46875 Combine like terms: -0.46875 + 0.46875 = 0.00000 0.00000 + t = 0.848366998 + 0.46875 t = 0.848366998 + 0.46875 Combine like terms: 0.848366998 + 0.46875 = 1.317116998 t = 1.317116998 Simplifying t = 1.317116998

Subproblem 2

t + -0.46875 = -0.848366998 Simplifying t + -0.46875 = -0.848366998 Reorder the terms: -0.46875 + t = -0.848366998 Solving -0.46875 + t = -0.848366998 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 = -0.848366998 + 0.46875 Combine like terms: -0.46875 + 0.46875 = 0.00000 0.00000 + t = -0.848366998 + 0.46875 t = -0.848366998 + 0.46875 Combine like terms: -0.848366998 + 0.46875 = -0.379616998 t = -0.379616998 Simplifying t = -0.379616998

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.317116998, -0.379616998}

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