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Simplifying t = 37.4 + 0.3t + -0.01t2 Solving t = 37.4 + 0.3t + -0.01t2 Solving for variable 't'. Reorder the terms: -37.4 + t + -0.3t + 0.01t2 = 37.4 + 0.3t + -0.01t2 + -37.4 + -0.3t + 0.01t2 Combine like terms: t + -0.3t = 0.7t -37.4 + 0.7t + 0.01t2 = 37.4 + 0.3t + -0.01t2 + -37.4 + -0.3t + 0.01t2 Reorder the terms: -37.4 + 0.7t + 0.01t2 = 37.4 + -37.4 + 0.3t + -0.3t + -0.01t2 + 0.01t2 Combine like terms: 37.4 + -37.4 = 0.0 -37.4 + 0.7t + 0.01t2 = 0.0 + 0.3t + -0.3t + -0.01t2 + 0.01t2 -37.4 + 0.7t + 0.01t2 = 0.3t + -0.3t + -0.01t2 + 0.01t2 Combine like terms: 0.3t + -0.3t = 0.0 -37.4 + 0.7t + 0.01t2 = 0.0 + -0.01t2 + 0.01t2 -37.4 + 0.7t + 0.01t2 = -0.01t2 + 0.01t2 Combine like terms: -0.01t2 + 0.01t2 = 0.00 -37.4 + 0.7t + 0.01t2 = 0.00 Begin completing the square. Divide all terms by 0.01 the coefficient of the squared term: Divide each side by '0.01'. -3740 + 70t + t2 = 0 Move the constant term to the right: Add '3740' to each side of the equation. -3740 + 70t + 3740 + t2 = 0 + 3740 Reorder the terms: -3740 + 3740 + 70t + t2 = 0 + 3740 Combine like terms: -3740 + 3740 = 0 0 + 70t + t2 = 0 + 3740 70t + t2 = 0 + 3740 Combine like terms: 0 + 3740 = 3740 70t + t2 = 3740 The t term is 70t. Take half its coefficient (35). Square it (1225) and add it to both sides. Add '1225' to each side of the equation. 70t + 1225 + t2 = 3740 + 1225 Reorder the terms: 1225 + 70t + t2 = 3740 + 1225 Combine like terms: 3740 + 1225 = 4965 1225 + 70t + t2 = 4965 Factor a perfect square on the left side: (t + 35)(t + 35) = 4965 Calculate the square root of the right side: 70.46275612 Break this problem into two subproblems by setting (t + 35) equal to 70.46275612 and -70.46275612.Subproblem 1
t + 35 = 70.46275612 Simplifying t + 35 = 70.46275612 Reorder the terms: 35 + t = 70.46275612 Solving 35 + t = 70.46275612 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + t = 70.46275612 + -35 Combine like terms: 35 + -35 = 0 0 + t = 70.46275612 + -35 t = 70.46275612 + -35 Combine like terms: 70.46275612 + -35 = 35.46275612 t = 35.46275612 Simplifying t = 35.46275612Subproblem 2
t + 35 = -70.46275612 Simplifying t + 35 = -70.46275612 Reorder the terms: 35 + t = -70.46275612 Solving 35 + t = -70.46275612 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + t = -70.46275612 + -35 Combine like terms: 35 + -35 = 0 0 + t = -70.46275612 + -35 t = -70.46275612 + -35 Combine like terms: -70.46275612 + -35 = -105.46275612 t = -105.46275612 Simplifying t = -105.46275612Solution
The solution to the problem is based on the solutions from the subproblems. t = {35.46275612, -105.46275612}
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