0=16t^2-800t+125

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Solution for 0=16t^2-800t+125 equation:


Simplifying
0 = 16t2 + -800t + 125

Reorder the terms:
0 = 125 + -800t + 16t2

Solving
0 = 125 + -800t + 16t2

Solving for variable 't'.

Combine like terms: 0 + -125 = -125
-125 + 800t + -16t2 = 125 + -800t + 16t2 + -125 + 800t + -16t2

Reorder the terms:
-125 + 800t + -16t2 = 125 + -125 + -800t + 800t + 16t2 + -16t2

Combine like terms: 125 + -125 = 0
-125 + 800t + -16t2 = 0 + -800t + 800t + 16t2 + -16t2
-125 + 800t + -16t2 = -800t + 800t + 16t2 + -16t2

Combine like terms: -800t + 800t = 0
-125 + 800t + -16t2 = 0 + 16t2 + -16t2
-125 + 800t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
-125 + 800t + -16t2 = 0

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

Divide each side by '-16'.
7.8125 + -50t + t2 = 0

Move the constant term to the right:

Add '-7.8125' to each side of the equation.
7.8125 + -50t + -7.8125 + t2 = 0 + -7.8125

Reorder the terms:
7.8125 + -7.8125 + -50t + t2 = 0 + -7.8125

Combine like terms: 7.8125 + -7.8125 = 0.0000
0.0000 + -50t + t2 = 0 + -7.8125
-50t + t2 = 0 + -7.8125

Combine like terms: 0 + -7.8125 = -7.8125
-50t + t2 = -7.8125

The t term is -50t.  Take half its coefficient (-25).
Square it (625) and add it to both sides.

Add '625' to each side of the equation.
-50t + 625 + t2 = -7.8125 + 625

Reorder the terms:
625 + -50t + t2 = -7.8125 + 625

Combine like terms: -7.8125 + 625 = 617.1875
625 + -50t + t2 = 617.1875

Factor a perfect square on the left side:
(t + -25)(t + -25) = 617.1875

Calculate the square root of the right side: 24.843258643

Break this problem into two subproblems by setting 
(t + -25) equal to 24.843258643 and -24.843258643.

Subproblem 1

t + -25 = 24.843258643 Simplifying t + -25 = 24.843258643 Reorder the terms: -25 + t = 24.843258643 Solving -25 + t = 24.843258643 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + t = 24.843258643 + 25 Combine like terms: -25 + 25 = 0 0 + t = 24.843258643 + 25 t = 24.843258643 + 25 Combine like terms: 24.843258643 + 25 = 49.843258643 t = 49.843258643 Simplifying t = 49.843258643

Subproblem 2

t + -25 = -24.843258643 Simplifying t + -25 = -24.843258643 Reorder the terms: -25 + t = -24.843258643 Solving -25 + t = -24.843258643 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + t = -24.843258643 + 25 Combine like terms: -25 + 25 = 0 0 + t = -24.843258643 + 25 t = -24.843258643 + 25 Combine like terms: -24.843258643 + 25 = 0.156741357 t = 0.156741357 Simplifying t = 0.156741357

Solution

The solution to the problem is based on the solutions from the subproblems. t = {49.843258643, 0.156741357}

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