0=16t^2-98t+49

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Solution for 0=16t^2-98t+49 equation:


Simplifying
0 = 16t2 + -98t + 49

Reorder the terms:
0 = 49 + -98t + 16t2

Solving
0 = 49 + -98t + 16t2

Solving for variable 't'.

Combine like terms: 0 + -49 = -49
-49 + 98t + -16t2 = 49 + -98t + 16t2 + -49 + 98t + -16t2

Reorder the terms:
-49 + 98t + -16t2 = 49 + -49 + -98t + 98t + 16t2 + -16t2

Combine like terms: 49 + -49 = 0
-49 + 98t + -16t2 = 0 + -98t + 98t + 16t2 + -16t2
-49 + 98t + -16t2 = -98t + 98t + 16t2 + -16t2

Combine like terms: -98t + 98t = 0
-49 + 98t + -16t2 = 0 + 16t2 + -16t2
-49 + 98t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
-49 + 98t + -16t2 = 0

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

Divide each side by '-16'.
3.0625 + -6.125t + t2 = 0

Move the constant term to the right:

Add '-3.0625' to each side of the equation.
3.0625 + -6.125t + -3.0625 + t2 = 0 + -3.0625

Reorder the terms:
3.0625 + -3.0625 + -6.125t + t2 = 0 + -3.0625

Combine like terms: 3.0625 + -3.0625 = 0.0000
0.0000 + -6.125t + t2 = 0 + -3.0625
-6.125t + t2 = 0 + -3.0625

Combine like terms: 0 + -3.0625 = -3.0625
-6.125t + t2 = -3.0625

The t term is -6.125t.  Take half its coefficient (-3.0625).
Square it (9.37890625) and add it to both sides.

Add '9.37890625' to each side of the equation.
-6.125t + 9.37890625 + t2 = -3.0625 + 9.37890625

Reorder the terms:
9.37890625 + -6.125t + t2 = -3.0625 + 9.37890625

Combine like terms: -3.0625 + 9.37890625 = 6.31640625
9.37890625 + -6.125t + t2 = 6.31640625

Factor a perfect square on the left side:
(t + -3.0625)(t + -3.0625) = 6.31640625

Calculate the square root of the right side: 2.513246158

Break this problem into two subproblems by setting 
(t + -3.0625) equal to 2.513246158 and -2.513246158.

Subproblem 1

t + -3.0625 = 2.513246158 Simplifying t + -3.0625 = 2.513246158 Reorder the terms: -3.0625 + t = 2.513246158 Solving -3.0625 + t = 2.513246158 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.0625' to each side of the equation. -3.0625 + 3.0625 + t = 2.513246158 + 3.0625 Combine like terms: -3.0625 + 3.0625 = 0.0000 0.0000 + t = 2.513246158 + 3.0625 t = 2.513246158 + 3.0625 Combine like terms: 2.513246158 + 3.0625 = 5.575746158 t = 5.575746158 Simplifying t = 5.575746158

Subproblem 2

t + -3.0625 = -2.513246158 Simplifying t + -3.0625 = -2.513246158 Reorder the terms: -3.0625 + t = -2.513246158 Solving -3.0625 + t = -2.513246158 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.0625' to each side of the equation. -3.0625 + 3.0625 + t = -2.513246158 + 3.0625 Combine like terms: -3.0625 + 3.0625 = 0.0000 0.0000 + t = -2.513246158 + 3.0625 t = -2.513246158 + 3.0625 Combine like terms: -2.513246158 + 3.0625 = 0.549253842 t = 0.549253842 Simplifying t = 0.549253842

Solution

The solution to the problem is based on the solutions from the subproblems. t = {5.575746158, 0.549253842}

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