-16t^2+201t+6=0

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Solution for -16t^2+201t+6=0 equation:


Simplifying
-16t2 + 201t + 6 = 0

Reorder the terms:
6 + 201t + -16t2 = 0

Solving
6 + 201t + -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'.
-0.375 + -12.5625t + t2 = 0

Move the constant term to the right:

Add '0.375' to each side of the equation.
-0.375 + -12.5625t + 0.375 + t2 = 0 + 0.375

Reorder the terms:
-0.375 + 0.375 + -12.5625t + t2 = 0 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + -12.5625t + t2 = 0 + 0.375
-12.5625t + t2 = 0 + 0.375

Combine like terms: 0 + 0.375 = 0.375
-12.5625t + t2 = 0.375

The t term is -12.5625t.  Take half its coefficient (-6.28125).
Square it (39.45410156) and add it to both sides.

Add '39.45410156' to each side of the equation.
-12.5625t + 39.45410156 + t2 = 0.375 + 39.45410156

Reorder the terms:
39.45410156 + -12.5625t + t2 = 0.375 + 39.45410156

Combine like terms: 0.375 + 39.45410156 = 39.82910156
39.45410156 + -12.5625t + t2 = 39.82910156

Factor a perfect square on the left side:
(t + -6.28125)(t + -6.28125) = 39.82910156

Calculate the square root of the right side: 6.31103015

Break this problem into two subproblems by setting 
(t + -6.28125) equal to 6.31103015 and -6.31103015.

Subproblem 1

t + -6.28125 = 6.31103015 Simplifying t + -6.28125 = 6.31103015 Reorder the terms: -6.28125 + t = 6.31103015 Solving -6.28125 + t = 6.31103015 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.28125' to each side of the equation. -6.28125 + 6.28125 + t = 6.31103015 + 6.28125 Combine like terms: -6.28125 + 6.28125 = 0.00000 0.00000 + t = 6.31103015 + 6.28125 t = 6.31103015 + 6.28125 Combine like terms: 6.31103015 + 6.28125 = 12.59228015 t = 12.59228015 Simplifying t = 12.59228015

Subproblem 2

t + -6.28125 = -6.31103015 Simplifying t + -6.28125 = -6.31103015 Reorder the terms: -6.28125 + t = -6.31103015 Solving -6.28125 + t = -6.31103015 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.28125' to each side of the equation. -6.28125 + 6.28125 + t = -6.31103015 + 6.28125 Combine like terms: -6.28125 + 6.28125 = 0.00000 0.00000 + t = -6.31103015 + 6.28125 t = -6.31103015 + 6.28125 Combine like terms: -6.31103015 + 6.28125 = -0.02978015 t = -0.02978015 Simplifying t = -0.02978015

Solution

The solution to the problem is based on the solutions from the subproblems. t = {12.59228015, -0.02978015}

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