2=-16t^2+127t

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Solution for 2=-16t^2+127t equation:


Simplifying
2 = -16t2 + 127t

Reorder the terms:
2 = 127t + -16t2

Solving
2 = 127t + -16t2

Solving for variable 't'.

Reorder the terms:
2 + -127t + 16t2 = 127t + -127t + -16t2 + 16t2

Combine like terms: 127t + -127t = 0
2 + -127t + 16t2 = 0 + -16t2 + 16t2
2 + -127t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
2 + -127t + 16t2 = 0

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

Divide each side by '16'.
0.125 + -7.9375t + t2 = 0

Move the constant term to the right:

Add '-0.125' to each side of the equation.
0.125 + -7.9375t + -0.125 + t2 = 0 + -0.125

Reorder the terms:
0.125 + -0.125 + -7.9375t + t2 = 0 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + -7.9375t + t2 = 0 + -0.125
-7.9375t + t2 = 0 + -0.125

Combine like terms: 0 + -0.125 = -0.125
-7.9375t + t2 = -0.125

The t term is -7.9375t.  Take half its coefficient (-3.96875).
Square it (15.75097656) and add it to both sides.

Add '15.75097656' to each side of the equation.
-7.9375t + 15.75097656 + t2 = -0.125 + 15.75097656

Reorder the terms:
15.75097656 + -7.9375t + t2 = -0.125 + 15.75097656

Combine like terms: -0.125 + 15.75097656 = 15.62597656
15.75097656 + -7.9375t + t2 = 15.62597656

Factor a perfect square on the left side:
(t + -3.96875)(t + -3.96875) = 15.62597656

Calculate the square root of the right side: 3.952970599

Break this problem into two subproblems by setting 
(t + -3.96875) equal to 3.952970599 and -3.952970599.

Subproblem 1

t + -3.96875 = 3.952970599 Simplifying t + -3.96875 = 3.952970599 Reorder the terms: -3.96875 + t = 3.952970599 Solving -3.96875 + t = 3.952970599 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.96875' to each side of the equation. -3.96875 + 3.96875 + t = 3.952970599 + 3.96875 Combine like terms: -3.96875 + 3.96875 = 0.00000 0.00000 + t = 3.952970599 + 3.96875 t = 3.952970599 + 3.96875 Combine like terms: 3.952970599 + 3.96875 = 7.921720599 t = 7.921720599 Simplifying t = 7.921720599

Subproblem 2

t + -3.96875 = -3.952970599 Simplifying t + -3.96875 = -3.952970599 Reorder the terms: -3.96875 + t = -3.952970599 Solving -3.96875 + t = -3.952970599 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.96875' to each side of the equation. -3.96875 + 3.96875 + t = -3.952970599 + 3.96875 Combine like terms: -3.96875 + 3.96875 = 0.00000 0.00000 + t = -3.952970599 + 3.96875 t = -3.952970599 + 3.96875 Combine like terms: -3.952970599 + 3.96875 = 0.015779401 t = 0.015779401 Simplifying t = 0.015779401

Solution

The solution to the problem is based on the solutions from the subproblems. t = {7.921720599, 0.015779401}

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