-16t^2+128t+5=0

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Solution for -16t^2+128t+5=0 equation:


Simplifying
-16t2 + 128t + 5 = 0

Reorder the terms:
5 + 128t + -16t2 = 0

Solving
5 + 128t + -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 + -8t + t2 = 0

Move the constant term to the right:

Add '0.3125' to each side of the equation.
-0.3125 + -8t + 0.3125 + t2 = 0 + 0.3125

Reorder the terms:
-0.3125 + 0.3125 + -8t + t2 = 0 + 0.3125

Combine like terms: -0.3125 + 0.3125 = 0.0000
0.0000 + -8t + t2 = 0 + 0.3125
-8t + t2 = 0 + 0.3125

Combine like terms: 0 + 0.3125 = 0.3125
-8t + t2 = 0.3125

The t term is -8t.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8t + 16 + t2 = 0.3125 + 16

Reorder the terms:
16 + -8t + t2 = 0.3125 + 16

Combine like terms: 0.3125 + 16 = 16.3125
16 + -8t + t2 = 16.3125

Factor a perfect square on the left side:
(t + -4)(t + -4) = 16.3125

Calculate the square root of the right side: 4.038873605

Break this problem into two subproblems by setting 
(t + -4) equal to 4.038873605 and -4.038873605.

Subproblem 1

t + -4 = 4.038873605 Simplifying t + -4 = 4.038873605 Reorder the terms: -4 + t = 4.038873605 Solving -4 + t = 4.038873605 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = 4.038873605 + 4 Combine like terms: -4 + 4 = 0 0 + t = 4.038873605 + 4 t = 4.038873605 + 4 Combine like terms: 4.038873605 + 4 = 8.038873605 t = 8.038873605 Simplifying t = 8.038873605

Subproblem 2

t + -4 = -4.038873605 Simplifying t + -4 = -4.038873605 Reorder the terms: -4 + t = -4.038873605 Solving -4 + t = -4.038873605 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = -4.038873605 + 4 Combine like terms: -4 + 4 = 0 0 + t = -4.038873605 + 4 t = -4.038873605 + 4 Combine like terms: -4.038873605 + 4 = -0.038873605 t = -0.038873605 Simplifying t = -0.038873605

Solution

The solution to the problem is based on the solutions from the subproblems. t = {8.038873605, -0.038873605}

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