16t^2-201t-93=0

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Solution for 16t^2-201t-93=0 equation:


Simplifying
16t2 + -201t + -93 = 0

Reorder the terms:
-93 + -201t + 16t2 = 0

Solving
-93 + -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'.
-5.8125 + -12.5625t + t2 = 0

Move the constant term to the right:

Add '5.8125' to each side of the equation.
-5.8125 + -12.5625t + 5.8125 + t2 = 0 + 5.8125

Reorder the terms:
-5.8125 + 5.8125 + -12.5625t + t2 = 0 + 5.8125

Combine like terms: -5.8125 + 5.8125 = 0.0000
0.0000 + -12.5625t + t2 = 0 + 5.8125
-12.5625t + t2 = 0 + 5.8125

Combine like terms: 0 + 5.8125 = 5.8125
-12.5625t + t2 = 5.8125

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 = 5.8125 + 39.45410156

Reorder the terms:
39.45410156 + -12.5625t + t2 = 5.8125 + 39.45410156

Combine like terms: 5.8125 + 39.45410156 = 45.26660156
39.45410156 + -12.5625t + t2 = 45.26660156

Factor a perfect square on the left side:
(t + -6.28125)(t + -6.28125) = 45.26660156

Calculate the square root of the right side: 6.728045895

Break this problem into two subproblems by setting 
(t + -6.28125) equal to 6.728045895 and -6.728045895.

Subproblem 1

t + -6.28125 = 6.728045895 Simplifying t + -6.28125 = 6.728045895 Reorder the terms: -6.28125 + t = 6.728045895 Solving -6.28125 + t = 6.728045895 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 = 6.728045895 + 6.28125 Combine like terms: -6.28125 + 6.28125 = 0.00000 0.00000 + t = 6.728045895 + 6.28125 t = 6.728045895 + 6.28125 Combine like terms: 6.728045895 + 6.28125 = 13.009295895 t = 13.009295895 Simplifying t = 13.009295895

Subproblem 2

t + -6.28125 = -6.728045895 Simplifying t + -6.28125 = -6.728045895 Reorder the terms: -6.28125 + t = -6.728045895 Solving -6.28125 + t = -6.728045895 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 = -6.728045895 + 6.28125 Combine like terms: -6.28125 + 6.28125 = 0.00000 0.00000 + t = -6.728045895 + 6.28125 t = -6.728045895 + 6.28125 Combine like terms: -6.728045895 + 6.28125 = -0.446795895 t = -0.446795895 Simplifying t = -0.446795895

Solution

The solution to the problem is based on the solutions from the subproblems. t = {13.009295895, -0.446795895}

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