-16t^2+56t+5=0

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Solution for -16t^2+56t+5=0 equation:


Simplifying
-16t2 + 56t + 5 = 0

Reorder the terms:
5 + 56t + -16t2 = 0

Solving
5 + 56t + -16t2 = 0

Solving for variable 't'.

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

Divide each side by '-16'.
-0.3125 + -3.5t + t2 = 0

Move the constant term to the right:

Add '0.3125' to each side of the equation.
-0.3125 + -3.5t + 0.3125 + t2 = 0 + 0.3125

Reorder the terms:
-0.3125 + 0.3125 + -3.5t + t2 = 0 + 0.3125

Combine like terms: -0.3125 + 0.3125 = 0.0000
0.0000 + -3.5t + t2 = 0 + 0.3125
-3.5t + t2 = 0 + 0.3125

Combine like terms: 0 + 0.3125 = 0.3125
-3.5t + t2 = 0.3125

The t term is -3.5t.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5t + 3.0625 + t2 = 0.3125 + 3.0625

Reorder the terms:
3.0625 + -3.5t + t2 = 0.3125 + 3.0625

Combine like terms: 0.3125 + 3.0625 = 3.375
3.0625 + -3.5t + t2 = 3.375

Factor a perfect square on the left side:
(t + -1.75)(t + -1.75) = 3.375

Calculate the square root of the right side: 1.837117307

Break this problem into two subproblems by setting 
(t + -1.75) equal to 1.837117307 and -1.837117307.

Subproblem 1

t + -1.75 = 1.837117307 Simplifying t + -1.75 = 1.837117307 Reorder the terms: -1.75 + t = 1.837117307 Solving -1.75 + t = 1.837117307 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + t = 1.837117307 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + t = 1.837117307 + 1.75 t = 1.837117307 + 1.75 Combine like terms: 1.837117307 + 1.75 = 3.587117307 t = 3.587117307 Simplifying t = 3.587117307

Subproblem 2

t + -1.75 = -1.837117307 Simplifying t + -1.75 = -1.837117307 Reorder the terms: -1.75 + t = -1.837117307 Solving -1.75 + t = -1.837117307 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + t = -1.837117307 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + t = -1.837117307 + 1.75 t = -1.837117307 + 1.75 Combine like terms: -1.837117307 + 1.75 = -0.087117307 t = -0.087117307 Simplifying t = -0.087117307

Solution

The solution to the problem is based on the solutions from the subproblems. t = {3.587117307, -0.087117307}

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