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Simplifying 2450 = 294t + -1(4.9t2) * 0.5 Remove parenthesis around (4.9t2) 2450 = 294t + -1 * 4.9t2 * 0.5 Reorder the terms for easier multiplication: 2450 = 294t + -1 * 4.9 * 0.5t2 Multiply -1 * 4.9 2450 = 294t + -4.9 * 0.5t2 Multiply -4.9 * 0.5 2450 = 294t + -2.45t2 Solving 2450 = 294t + -2.45t2 Solving for variable 't'. Reorder the terms: 2450 + -294t + 2.45t2 = 294t + -294t + -2.45t2 + 2.45t2 Combine like terms: 294t + -294t = 0 2450 + -294t + 2.45t2 = 0 + -2.45t2 + 2.45t2 2450 + -294t + 2.45t2 = -2.45t2 + 2.45t2 Combine like terms: -2.45t2 + 2.45t2 = 0.00 2450 + -294t + 2.45t2 = 0.00 Begin completing the square. Divide all terms by 2.45 the coefficient of the squared term: Divide each side by '2.45'. 1000 + -120t + t2 = 0 Move the constant term to the right: Add '-1000' to each side of the equation. 1000 + -120t + -1000 + t2 = 0 + -1000 Reorder the terms: 1000 + -1000 + -120t + t2 = 0 + -1000 Combine like terms: 1000 + -1000 = 0 0 + -120t + t2 = 0 + -1000 -120t + t2 = 0 + -1000 Combine like terms: 0 + -1000 = -1000 -120t + t2 = -1000 The t term is -120t. Take half its coefficient (-60). Square it (3600) and add it to both sides. Add '3600' to each side of the equation. -120t + 3600 + t2 = -1000 + 3600 Reorder the terms: 3600 + -120t + t2 = -1000 + 3600 Combine like terms: -1000 + 3600 = 2600 3600 + -120t + t2 = 2600 Factor a perfect square on the left side: (t + -60)(t + -60) = 2600 Calculate the square root of the right side: 50.990195136 Break this problem into two subproblems by setting (t + -60) equal to 50.990195136 and -50.990195136.Subproblem 1
t + -60 = 50.990195136 Simplifying t + -60 = 50.990195136 Reorder the terms: -60 + t = 50.990195136 Solving -60 + t = 50.990195136 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '60' to each side of the equation. -60 + 60 + t = 50.990195136 + 60 Combine like terms: -60 + 60 = 0 0 + t = 50.990195136 + 60 t = 50.990195136 + 60 Combine like terms: 50.990195136 + 60 = 110.990195136 t = 110.990195136 Simplifying t = 110.990195136Subproblem 2
t + -60 = -50.990195136 Simplifying t + -60 = -50.990195136 Reorder the terms: -60 + t = -50.990195136 Solving -60 + t = -50.990195136 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '60' to each side of the equation. -60 + 60 + t = -50.990195136 + 60 Combine like terms: -60 + 60 = 0 0 + t = -50.990195136 + 60 t = -50.990195136 + 60 Combine like terms: -50.990195136 + 60 = 9.009804864 t = 9.009804864 Simplifying t = 9.009804864Solution
The solution to the problem is based on the solutions from the subproblems. t = {110.990195136, 9.009804864}
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