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Simplifying 0 = 250 + 63(t) + -4.9(t2) Solving 0 = 250 + 63t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -250 = -250 -250 + -63t + 4.9t2 = 250 + 63t + -4.9t2 + -250 + -63t + 4.9t2 Reorder the terms: -250 + -63t + 4.9t2 = 250 + -250 + 63t + -63t + -4.9t2 + 4.9t2 Combine like terms: 250 + -250 = 0 -250 + -63t + 4.9t2 = 0 + 63t + -63t + -4.9t2 + 4.9t2 -250 + -63t + 4.9t2 = 63t + -63t + -4.9t2 + 4.9t2 Combine like terms: 63t + -63t = 0 -250 + -63t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -250 + -63t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -250 + -63t + 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'. -51.02040816 + -12.85714286t + t2 = 0 Move the constant term to the right: Add '51.02040816' to each side of the equation. -51.02040816 + -12.85714286t + 51.02040816 + t2 = 0 + 51.02040816 Reorder the terms: -51.02040816 + 51.02040816 + -12.85714286t + t2 = 0 + 51.02040816 Combine like terms: -51.02040816 + 51.02040816 = 0.00000000 0.00000000 + -12.85714286t + t2 = 0 + 51.02040816 -12.85714286t + t2 = 0 + 51.02040816 Combine like terms: 0 + 51.02040816 = 51.02040816 -12.85714286t + t2 = 51.02040816 The t term is -12.85714286t. Take half its coefficient (-6.42857143). Square it (41.32653063) and add it to both sides. Add '41.32653063' to each side of the equation. -12.85714286t + 41.32653063 + t2 = 51.02040816 + 41.32653063 Reorder the terms: 41.32653063 + -12.85714286t + t2 = 51.02040816 + 41.32653063 Combine like terms: 51.02040816 + 41.32653063 = 92.34693879 41.32653063 + -12.85714286t + t2 = 92.34693879 Factor a perfect square on the left side: (t + -6.42857143)(t + -6.42857143) = 92.34693879 Calculate the square root of the right side: 9.609731463 Break this problem into two subproblems by setting (t + -6.42857143) equal to 9.609731463 and -9.609731463.Subproblem 1
t + -6.42857143 = 9.609731463 Simplifying t + -6.42857143 = 9.609731463 Reorder the terms: -6.42857143 + t = 9.609731463 Solving -6.42857143 + t = 9.609731463 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.42857143' to each side of the equation. -6.42857143 + 6.42857143 + t = 9.609731463 + 6.42857143 Combine like terms: -6.42857143 + 6.42857143 = 0.00000000 0.00000000 + t = 9.609731463 + 6.42857143 t = 9.609731463 + 6.42857143 Combine like terms: 9.609731463 + 6.42857143 = 16.038302893 t = 16.038302893 Simplifying t = 16.038302893Subproblem 2
t + -6.42857143 = -9.609731463 Simplifying t + -6.42857143 = -9.609731463 Reorder the terms: -6.42857143 + t = -9.609731463 Solving -6.42857143 + t = -9.609731463 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.42857143' to each side of the equation. -6.42857143 + 6.42857143 + t = -9.609731463 + 6.42857143 Combine like terms: -6.42857143 + 6.42857143 = 0.00000000 0.00000000 + t = -9.609731463 + 6.42857143 t = -9.609731463 + 6.42857143 Combine like terms: -9.609731463 + 6.42857143 = -3.181160033 t = -3.181160033 Simplifying t = -3.181160033Solution
The solution to the problem is based on the solutions from the subproblems. t = {16.038302893, -3.181160033}
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