0=-16t^2+25t+4

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Solution for 0=-16t^2+25t+4 equation:


Simplifying
0 = -16t2 + 25t + 4

Reorder the terms:
0 = 4 + 25t + -16t2

Solving
0 = 4 + 25t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -4 = -4
-4 + -25t + 16t2 = 4 + 25t + -16t2 + -4 + -25t + 16t2

Reorder the terms:
-4 + -25t + 16t2 = 4 + -4 + 25t + -25t + -16t2 + 16t2

Combine like terms: 4 + -4 = 0
-4 + -25t + 16t2 = 0 + 25t + -25t + -16t2 + 16t2
-4 + -25t + 16t2 = 25t + -25t + -16t2 + 16t2

Combine like terms: 25t + -25t = 0
-4 + -25t + 16t2 = 0 + -16t2 + 16t2
-4 + -25t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-4 + -25t + 16t2 = 0

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

Divide each side by '16'.
-0.25 + -1.5625t + t2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -1.5625t + 0.25 + t2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -1.5625t + t2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -1.5625t + t2 = 0 + 0.25
-1.5625t + t2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-1.5625t + t2 = 0.25

The t term is -1.5625t.  Take half its coefficient (-0.78125).
Square it (0.6103515625) and add it to both sides.

Add '0.6103515625' to each side of the equation.
-1.5625t + 0.6103515625 + t2 = 0.25 + 0.6103515625

Reorder the terms:
0.6103515625 + -1.5625t + t2 = 0.25 + 0.6103515625

Combine like terms: 0.25 + 0.6103515625 = 0.8603515625
0.6103515625 + -1.5625t + t2 = 0.8603515625

Factor a perfect square on the left side:
(t + -0.78125)(t + -0.78125) = 0.8603515625

Calculate the square root of the right side: 0.92755138

Break this problem into two subproblems by setting 
(t + -0.78125) equal to 0.92755138 and -0.92755138.

Subproblem 1

t + -0.78125 = 0.92755138 Simplifying t + -0.78125 = 0.92755138 Reorder the terms: -0.78125 + t = 0.92755138 Solving -0.78125 + t = 0.92755138 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.78125' to each side of the equation. -0.78125 + 0.78125 + t = 0.92755138 + 0.78125 Combine like terms: -0.78125 + 0.78125 = 0.00000 0.00000 + t = 0.92755138 + 0.78125 t = 0.92755138 + 0.78125 Combine like terms: 0.92755138 + 0.78125 = 1.70880138 t = 1.70880138 Simplifying t = 1.70880138

Subproblem 2

t + -0.78125 = -0.92755138 Simplifying t + -0.78125 = -0.92755138 Reorder the terms: -0.78125 + t = -0.92755138 Solving -0.78125 + t = -0.92755138 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.78125' to each side of the equation. -0.78125 + 0.78125 + t = -0.92755138 + 0.78125 Combine like terms: -0.78125 + 0.78125 = 0.00000 0.00000 + t = -0.92755138 + 0.78125 t = -0.92755138 + 0.78125 Combine like terms: -0.92755138 + 0.78125 = -0.14630138 t = -0.14630138 Simplifying t = -0.14630138

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.70880138, -0.14630138}

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