0=15+8t-5t^2

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Solution for 0=15+8t-5t^2 equation:


Simplifying
0 = 15 + 8t + -5t2

Solving
0 = 15 + 8t + -5t2

Solving for variable 't'.

Combine like terms: 0 + -15 = -15
-15 + -8t + 5t2 = 15 + 8t + -5t2 + -15 + -8t + 5t2

Reorder the terms:
-15 + -8t + 5t2 = 15 + -15 + 8t + -8t + -5t2 + 5t2

Combine like terms: 15 + -15 = 0
-15 + -8t + 5t2 = 0 + 8t + -8t + -5t2 + 5t2
-15 + -8t + 5t2 = 8t + -8t + -5t2 + 5t2

Combine like terms: 8t + -8t = 0
-15 + -8t + 5t2 = 0 + -5t2 + 5t2
-15 + -8t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
-15 + -8t + 5t2 = 0

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

Divide each side by '5'.
-3 + -1.6t + t2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -1.6t + 3 + t2 = 0 + 3

Reorder the terms:
-3 + 3 + -1.6t + t2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1.6t + t2 = 0 + 3
-1.6t + t2 = 0 + 3

Combine like terms: 0 + 3 = 3
-1.6t + t2 = 3

The t term is -1.6t.  Take half its coefficient (-0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
-1.6t + 0.64 + t2 = 3 + 0.64

Reorder the terms:
0.64 + -1.6t + t2 = 3 + 0.64

Combine like terms: 3 + 0.64 = 3.64
0.64 + -1.6t + t2 = 3.64

Factor a perfect square on the left side:
(t + -0.8)(t + -0.8) = 3.64

Calculate the square root of the right side: 1.907878403

Break this problem into two subproblems by setting 
(t + -0.8) equal to 1.907878403 and -1.907878403.

Subproblem 1

t + -0.8 = 1.907878403 Simplifying t + -0.8 = 1.907878403 Reorder the terms: -0.8 + t = 1.907878403 Solving -0.8 + t = 1.907878403 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + t = 1.907878403 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + t = 1.907878403 + 0.8 t = 1.907878403 + 0.8 Combine like terms: 1.907878403 + 0.8 = 2.707878403 t = 2.707878403 Simplifying t = 2.707878403

Subproblem 2

t + -0.8 = -1.907878403 Simplifying t + -0.8 = -1.907878403 Reorder the terms: -0.8 + t = -1.907878403 Solving -0.8 + t = -1.907878403 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + t = -1.907878403 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + t = -1.907878403 + 0.8 t = -1.907878403 + 0.8 Combine like terms: -1.907878403 + 0.8 = -1.107878403 t = -1.107878403 Simplifying t = -1.107878403

Solution

The solution to the problem is based on the solutions from the subproblems. t = {2.707878403, -1.107878403}

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