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Simplifying 69.85 = -4.9t2 + 36.85t + 0.61 Reorder the terms: 69.85 = 0.61 + 36.85t + -4.9t2 Solving 69.85 = 0.61 + 36.85t + -4.9t2 Solving for variable 't'. Combine like terms: 69.85 + -0.61 = 69.24 69.24 + -36.85t + 4.9t2 = 0.61 + 36.85t + -4.9t2 + -0.61 + -36.85t + 4.9t2 Reorder the terms: 69.24 + -36.85t + 4.9t2 = 0.61 + -0.61 + 36.85t + -36.85t + -4.9t2 + 4.9t2 Combine like terms: 0.61 + -0.61 = 0.00 69.24 + -36.85t + 4.9t2 = 0.00 + 36.85t + -36.85t + -4.9t2 + 4.9t2 69.24 + -36.85t + 4.9t2 = 36.85t + -36.85t + -4.9t2 + 4.9t2 Combine like terms: 36.85t + -36.85t = 0.00 69.24 + -36.85t + 4.9t2 = 0.00 + -4.9t2 + 4.9t2 69.24 + -36.85t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 69.24 + -36.85t + 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'. 14.13061224 + -7.520408163t + t2 = 0 Move the constant term to the right: Add '-14.13061224' to each side of the equation. 14.13061224 + -7.520408163t + -14.13061224 + t2 = 0 + -14.13061224 Reorder the terms: 14.13061224 + -14.13061224 + -7.520408163t + t2 = 0 + -14.13061224 Combine like terms: 14.13061224 + -14.13061224 = 0.00000000 0.00000000 + -7.520408163t + t2 = 0 + -14.13061224 -7.520408163t + t2 = 0 + -14.13061224 Combine like terms: 0 + -14.13061224 = -14.13061224 -7.520408163t + t2 = -14.13061224 The t term is -7.520408163t. Take half its coefficient (-3.760204082). Square it (14.13913474) and add it to both sides. Add '14.13913474' to each side of the equation. -7.520408163t + 14.13913474 + t2 = -14.13061224 + 14.13913474 Reorder the terms: 14.13913474 + -7.520408163t + t2 = -14.13061224 + 14.13913474 Combine like terms: -14.13061224 + 14.13913474 = 0.0085225 14.13913474 + -7.520408163t + t2 = 0.0085225 Factor a perfect square on the left side: (t + -3.760204082)(t + -3.760204082) = 0.0085225 Calculate the square root of the right side: 0.092317387 Break this problem into two subproblems by setting (t + -3.760204082) equal to 0.092317387 and -0.092317387.Subproblem 1
t + -3.760204082 = 0.092317387 Simplifying t + -3.760204082 = 0.092317387 Reorder the terms: -3.760204082 + t = 0.092317387 Solving -3.760204082 + t = 0.092317387 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.760204082' to each side of the equation. -3.760204082 + 3.760204082 + t = 0.092317387 + 3.760204082 Combine like terms: -3.760204082 + 3.760204082 = 0.000000000 0.000000000 + t = 0.092317387 + 3.760204082 t = 0.092317387 + 3.760204082 Combine like terms: 0.092317387 + 3.760204082 = 3.852521469 t = 3.852521469 Simplifying t = 3.852521469Subproblem 2
t + -3.760204082 = -0.092317387 Simplifying t + -3.760204082 = -0.092317387 Reorder the terms: -3.760204082 + t = -0.092317387 Solving -3.760204082 + t = -0.092317387 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.760204082' to each side of the equation. -3.760204082 + 3.760204082 + t = -0.092317387 + 3.760204082 Combine like terms: -3.760204082 + 3.760204082 = 0.000000000 0.000000000 + t = -0.092317387 + 3.760204082 t = -0.092317387 + 3.760204082 Combine like terms: -0.092317387 + 3.760204082 = 3.667886695 t = 3.667886695 Simplifying t = 3.667886695Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.852521469, 3.667886695}
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