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Simplifying 0 = 4.9t2 + 345t + -2070 Reorder the terms: 0 = -2070 + 345t + 4.9t2 Solving 0 = -2070 + 345t + 4.9t2 Solving for variable 't'. Combine like terms: 0 + 2070 = 2070 2070 + -345t + -4.9t2 = -2070 + 345t + 4.9t2 + 2070 + -345t + -4.9t2 Reorder the terms: 2070 + -345t + -4.9t2 = -2070 + 2070 + 345t + -345t + 4.9t2 + -4.9t2 Combine like terms: -2070 + 2070 = 0 2070 + -345t + -4.9t2 = 0 + 345t + -345t + 4.9t2 + -4.9t2 2070 + -345t + -4.9t2 = 345t + -345t + 4.9t2 + -4.9t2 Combine like terms: 345t + -345t = 0 2070 + -345t + -4.9t2 = 0 + 4.9t2 + -4.9t2 2070 + -345t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 2070 + -345t + -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'. -422.4489796 + 70.40816327t + t2 = 0 Move the constant term to the right: Add '422.4489796' to each side of the equation. -422.4489796 + 70.40816327t + 422.4489796 + t2 = 0 + 422.4489796 Reorder the terms: -422.4489796 + 422.4489796 + 70.40816327t + t2 = 0 + 422.4489796 Combine like terms: -422.4489796 + 422.4489796 = 0.0000000 0.0000000 + 70.40816327t + t2 = 0 + 422.4489796 70.40816327t + t2 = 0 + 422.4489796 Combine like terms: 0 + 422.4489796 = 422.4489796 70.40816327t + t2 = 422.4489796 The t term is 70.40816327t. Take half its coefficient (35.20408164). Square it (1239.327364) and add it to both sides. Add '1239.327364' to each side of the equation. 70.40816327t + 1239.327364 + t2 = 422.4489796 + 1239.327364 Reorder the terms: 1239.327364 + 70.40816327t + t2 = 422.4489796 + 1239.327364 Combine like terms: 422.4489796 + 1239.327364 = 1661.7763436 1239.327364 + 70.40816327t + t2 = 1661.7763436 Factor a perfect square on the left side: (t + 35.20408164)(t + 35.20408164) = 1661.7763436 Calculate the square root of the right side: 40.764891066 Break this problem into two subproblems by setting (t + 35.20408164) equal to 40.764891066 and -40.764891066.Subproblem 1
t + 35.20408164 = 40.764891066 Simplifying t + 35.20408164 = 40.764891066 Reorder the terms: 35.20408164 + t = 40.764891066 Solving 35.20408164 + t = 40.764891066 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-35.20408164' to each side of the equation. 35.20408164 + -35.20408164 + t = 40.764891066 + -35.20408164 Combine like terms: 35.20408164 + -35.20408164 = 0.00000000 0.00000000 + t = 40.764891066 + -35.20408164 t = 40.764891066 + -35.20408164 Combine like terms: 40.764891066 + -35.20408164 = 5.560809426 t = 5.560809426 Simplifying t = 5.560809426Subproblem 2
t + 35.20408164 = -40.764891066 Simplifying t + 35.20408164 = -40.764891066 Reorder the terms: 35.20408164 + t = -40.764891066 Solving 35.20408164 + t = -40.764891066 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-35.20408164' to each side of the equation. 35.20408164 + -35.20408164 + t = -40.764891066 + -35.20408164 Combine like terms: 35.20408164 + -35.20408164 = 0.00000000 0.00000000 + t = -40.764891066 + -35.20408164 t = -40.764891066 + -35.20408164 Combine like terms: -40.764891066 + -35.20408164 = -75.968972706 t = -75.968972706 Simplifying t = -75.968972706Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.560809426, -75.968972706}
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