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Simplifying 20 = -4.9t2 + 30t + 3 Reorder the terms: 20 = 3 + 30t + -4.9t2 Solving 20 = 3 + 30t + -4.9t2 Solving for variable 't'. Combine like terms: 20 + -3 = 17 17 + -30t + 4.9t2 = 3 + 30t + -4.9t2 + -3 + -30t + 4.9t2 Reorder the terms: 17 + -30t + 4.9t2 = 3 + -3 + 30t + -30t + -4.9t2 + 4.9t2 Combine like terms: 3 + -3 = 0 17 + -30t + 4.9t2 = 0 + 30t + -30t + -4.9t2 + 4.9t2 17 + -30t + 4.9t2 = 30t + -30t + -4.9t2 + 4.9t2 Combine like terms: 30t + -30t = 0 17 + -30t + 4.9t2 = 0 + -4.9t2 + 4.9t2 17 + -30t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 17 + -30t + 4.9t2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. 3.469387755 + -6.12244898t + t2 = 0 Move the constant term to the right: Add '-3.469387755' to each side of the equation. 3.469387755 + -6.12244898t + -3.469387755 + t2 = 0 + -3.469387755 Reorder the terms: 3.469387755 + -3.469387755 + -6.12244898t + t2 = 0 + -3.469387755 Combine like terms: 3.469387755 + -3.469387755 = 0.000000000 0.000000000 + -6.12244898t + t2 = 0 + -3.469387755 -6.12244898t + t2 = 0 + -3.469387755 Combine like terms: 0 + -3.469387755 = -3.469387755 -6.12244898t + t2 = -3.469387755 The t term is -6.12244898t. Take half its coefficient (-3.06122449). Square it (9.371095378) and add it to both sides. Add '9.371095378' to each side of the equation. -6.12244898t + 9.371095378 + t2 = -3.469387755 + 9.371095378 Reorder the terms: 9.371095378 + -6.12244898t + t2 = -3.469387755 + 9.371095378 Combine like terms: -3.469387755 + 9.371095378 = 5.901707623 9.371095378 + -6.12244898t + t2 = 5.901707623 Factor a perfect square on the left side: (t + -3.06122449)(t + -3.06122449) = 5.901707623 Calculate the square root of the right side: 2.429343044 Break this problem into two subproblems by setting (t + -3.06122449) equal to 2.429343044 and -2.429343044.Subproblem 1
t + -3.06122449 = 2.429343044 Simplifying t + -3.06122449 = 2.429343044 Reorder the terms: -3.06122449 + t = 2.429343044 Solving -3.06122449 + t = 2.429343044 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.06122449' to each side of the equation. -3.06122449 + 3.06122449 + t = 2.429343044 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + t = 2.429343044 + 3.06122449 t = 2.429343044 + 3.06122449 Combine like terms: 2.429343044 + 3.06122449 = 5.490567534 t = 5.490567534 Simplifying t = 5.490567534Subproblem 2
t + -3.06122449 = -2.429343044 Simplifying t + -3.06122449 = -2.429343044 Reorder the terms: -3.06122449 + t = -2.429343044 Solving -3.06122449 + t = -2.429343044 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.06122449' to each side of the equation. -3.06122449 + 3.06122449 + t = -2.429343044 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + t = -2.429343044 + 3.06122449 t = -2.429343044 + 3.06122449 Combine like terms: -2.429343044 + 3.06122449 = 0.631881446 t = 0.631881446 Simplifying t = 0.631881446Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.490567534, 0.631881446}
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