(4.905t^2)-(16t)+6=0

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Solution for (4.905t^2)-(16t)+6=0 equation:


Simplifying
(4.905t2) + -1(16t) + 6 = 0

Remove parenthesis around (16t)
(4.905t2) + -1 * 16t + 6 = 0

Multiply -1 * 16
(4.905t2) + -16t + 6 = 0

Reorder the terms:
6 + -16t + (4.905t2) = 0

Solving
6 + -16t + (4.905t2) = 0

Solving for variable 't'.

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

Divide each side by '4.905'.
1.22324159 + -3.261977574t + t2 = 0

Move the constant term to the right:

Add '-1.22324159' to each side of the equation.
1.22324159 + -3.261977574t + -1.22324159 + t2 = 0 + -1.22324159

Reorder the terms:
1.22324159 + -1.22324159 + -3.261977574t + t2 = 0 + -1.22324159

Combine like terms: 1.22324159 + -1.22324159 = 0.00000000
0.00000000 + -3.261977574t + t2 = 0 + -1.22324159
-3.261977574t + t2 = 0 + -1.22324159

Combine like terms: 0 + -1.22324159 = -1.22324159
-3.261977574t + t2 = -1.22324159

The t term is -3.261977574t.  Take half its coefficient (-1.630988787).
Square it (2.660124423) and add it to both sides.

Add '2.660124423' to each side of the equation.
-3.261977574t + 2.660124423 + t2 = -1.22324159 + 2.660124423

Reorder the terms:
2.660124423 + -3.261977574t + t2 = -1.22324159 + 2.660124423

Combine like terms: -1.22324159 + 2.660124423 = 1.436882833
2.660124423 + -3.261977574t + t2 = 1.436882833

Factor a perfect square on the left side:
((t) + -1.630988787)((t) + -1.630988787) = 1.436882833

Calculate the square root of the right side: 1.198700477

Break this problem into two subproblems by setting 
((t) + -1.630988787) equal to 1.198700477 and -1.198700477.

Subproblem 1

(t) + -1.630988787 = 1.198700477 Simplifying (t) + -1.630988787 = 1.198700477 t + -1.630988787 = 1.198700477 Reorder the terms: -1.630988787 + t = 1.198700477 Solving -1.630988787 + t = 1.198700477 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.630988787' to each side of the equation. -1.630988787 + 1.630988787 + t = 1.198700477 + 1.630988787 Combine like terms: -1.630988787 + 1.630988787 = 0.000000000 0.000000000 + t = 1.198700477 + 1.630988787 t = 1.198700477 + 1.630988787 Combine like terms: 1.198700477 + 1.630988787 = 2.829689264 t = 2.829689264 Simplifying t = 2.829689264

Subproblem 2

(t) + -1.630988787 = -1.198700477 Simplifying (t) + -1.630988787 = -1.198700477 t + -1.630988787 = -1.198700477 Reorder the terms: -1.630988787 + t = -1.198700477 Solving -1.630988787 + t = -1.198700477 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.630988787' to each side of the equation. -1.630988787 + 1.630988787 + t = -1.198700477 + 1.630988787 Combine like terms: -1.630988787 + 1.630988787 = 0.000000000 0.000000000 + t = -1.198700477 + 1.630988787 t = -1.198700477 + 1.630988787 Combine like terms: -1.198700477 + 1.630988787 = 0.43228831 t = 0.43228831 Simplifying t = 0.43228831

Solution

The solution to the problem is based on the solutions from the subproblems. t = {2.829689264, 0.43228831}

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