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Simplifying 4.9t2 + -20.44t + 15 = 0 Reorder the terms: 15 + -20.44t + 4.9t2 = 0 Solving 15 + -20.44t + 4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. 3.06122449 + -4.171428571t + t2 = 0 Move the constant term to the right: Add '-3.06122449' to each side of the equation. 3.06122449 + -4.171428571t + -3.06122449 + t2 = 0 + -3.06122449 Reorder the terms: 3.06122449 + -3.06122449 + -4.171428571t + t2 = 0 + -3.06122449 Combine like terms: 3.06122449 + -3.06122449 = 0.00000000 0.00000000 + -4.171428571t + t2 = 0 + -3.06122449 -4.171428571t + t2 = 0 + -3.06122449 Combine like terms: 0 + -3.06122449 = -3.06122449 -4.171428571t + t2 = -3.06122449 The t term is -4.171428571t. Take half its coefficient (-2.085714286). Square it (4.350204083) and add it to both sides. Add '4.350204083' to each side of the equation. -4.171428571t + 4.350204083 + t2 = -3.06122449 + 4.350204083 Reorder the terms: 4.350204083 + -4.171428571t + t2 = -3.06122449 + 4.350204083 Combine like terms: -3.06122449 + 4.350204083 = 1.288979593 4.350204083 + -4.171428571t + t2 = 1.288979593 Factor a perfect square on the left side: (t + -2.085714286)(t + -2.085714286) = 1.288979593 Calculate the square root of the right side: 1.135332371 Break this problem into two subproblems by setting (t + -2.085714286) equal to 1.135332371 and -1.135332371.Subproblem 1
t + -2.085714286 = 1.135332371 Simplifying t + -2.085714286 = 1.135332371 Reorder the terms: -2.085714286 + t = 1.135332371 Solving -2.085714286 + t = 1.135332371 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.085714286' to each side of the equation. -2.085714286 + 2.085714286 + t = 1.135332371 + 2.085714286 Combine like terms: -2.085714286 + 2.085714286 = 0.000000000 0.000000000 + t = 1.135332371 + 2.085714286 t = 1.135332371 + 2.085714286 Combine like terms: 1.135332371 + 2.085714286 = 3.221046657 t = 3.221046657 Simplifying t = 3.221046657Subproblem 2
t + -2.085714286 = -1.135332371 Simplifying t + -2.085714286 = -1.135332371 Reorder the terms: -2.085714286 + t = -1.135332371 Solving -2.085714286 + t = -1.135332371 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.085714286' to each side of the equation. -2.085714286 + 2.085714286 + t = -1.135332371 + 2.085714286 Combine like terms: -2.085714286 + 2.085714286 = 0.000000000 0.000000000 + t = -1.135332371 + 2.085714286 t = -1.135332371 + 2.085714286 Combine like terms: -1.135332371 + 2.085714286 = 0.950381915 t = 0.950381915 Simplifying t = 0.950381915Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.221046657, 0.950381915}
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