0=-16t^2+5t+1255

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Solution for 0=-16t^2+5t+1255 equation:


Simplifying
0 = -16t2 + 5t + 1255

Reorder the terms:
0 = 1255 + 5t + -16t2

Solving
0 = 1255 + 5t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -1255 = -1255
-1255 + -5t + 16t2 = 1255 + 5t + -16t2 + -1255 + -5t + 16t2

Reorder the terms:
-1255 + -5t + 16t2 = 1255 + -1255 + 5t + -5t + -16t2 + 16t2

Combine like terms: 1255 + -1255 = 0
-1255 + -5t + 16t2 = 0 + 5t + -5t + -16t2 + 16t2
-1255 + -5t + 16t2 = 5t + -5t + -16t2 + 16t2

Combine like terms: 5t + -5t = 0
-1255 + -5t + 16t2 = 0 + -16t2 + 16t2
-1255 + -5t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-1255 + -5t + 16t2 = 0

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

Divide each side by '16'.
-78.4375 + -0.3125t + t2 = 0

Move the constant term to the right:

Add '78.4375' to each side of the equation.
-78.4375 + -0.3125t + 78.4375 + t2 = 0 + 78.4375

Reorder the terms:
-78.4375 + 78.4375 + -0.3125t + t2 = 0 + 78.4375

Combine like terms: -78.4375 + 78.4375 = 0.0000
0.0000 + -0.3125t + t2 = 0 + 78.4375
-0.3125t + t2 = 0 + 78.4375

Combine like terms: 0 + 78.4375 = 78.4375
-0.3125t + t2 = 78.4375

The t term is -0.3125t.  Take half its coefficient (-0.15625).
Square it (0.0244140625) and add it to both sides.

Add '0.0244140625' to each side of the equation.
-0.3125t + 0.0244140625 + t2 = 78.4375 + 0.0244140625

Reorder the terms:
0.0244140625 + -0.3125t + t2 = 78.4375 + 0.0244140625

Combine like terms: 78.4375 + 0.0244140625 = 78.4619140625
0.0244140625 + -0.3125t + t2 = 78.4619140625

Factor a perfect square on the left side:
(t + -0.15625)(t + -0.15625) = 78.4619140625

Calculate the square root of the right side: 8.857872999

Break this problem into two subproblems by setting 
(t + -0.15625) equal to 8.857872999 and -8.857872999.

Subproblem 1

t + -0.15625 = 8.857872999 Simplifying t + -0.15625 = 8.857872999 Reorder the terms: -0.15625 + t = 8.857872999 Solving -0.15625 + t = 8.857872999 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.15625' to each side of the equation. -0.15625 + 0.15625 + t = 8.857872999 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + t = 8.857872999 + 0.15625 t = 8.857872999 + 0.15625 Combine like terms: 8.857872999 + 0.15625 = 9.014122999 t = 9.014122999 Simplifying t = 9.014122999

Subproblem 2

t + -0.15625 = -8.857872999 Simplifying t + -0.15625 = -8.857872999 Reorder the terms: -0.15625 + t = -8.857872999 Solving -0.15625 + t = -8.857872999 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.15625' to each side of the equation. -0.15625 + 0.15625 + t = -8.857872999 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + t = -8.857872999 + 0.15625 t = -8.857872999 + 0.15625 Combine like terms: -8.857872999 + 0.15625 = -8.701622999 t = -8.701622999 Simplifying t = -8.701622999

Solution

The solution to the problem is based on the solutions from the subproblems. t = {9.014122999, -8.701622999}

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