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Simplifying 4.905t2 + -20t + 15 = 0 Reorder the terms: 15 + -20t + 4.905t2 = 0 Solving 15 + -20t + 4.905t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.905 the coefficient of the squared term: Divide each side by '4.905'. 3.058103976 + -4.077471967t + t2 = 0 Move the constant term to the right: Add '-3.058103976' to each side of the equation. 3.058103976 + -4.077471967t + -3.058103976 + t2 = 0 + -3.058103976 Reorder the terms: 3.058103976 + -3.058103976 + -4.077471967t + t2 = 0 + -3.058103976 Combine like terms: 3.058103976 + -3.058103976 = 0.000000000 0.000000000 + -4.077471967t + t2 = 0 + -3.058103976 -4.077471967t + t2 = 0 + -3.058103976 Combine like terms: 0 + -3.058103976 = -3.058103976 -4.077471967t + t2 = -3.058103976 The t term is -4.077471967t. Take half its coefficient (-2.038735984). Square it (4.156444412) and add it to both sides. Add '4.156444412' to each side of the equation. -4.077471967t + 4.156444412 + t2 = -3.058103976 + 4.156444412 Reorder the terms: 4.156444412 + -4.077471967t + t2 = -3.058103976 + 4.156444412 Combine like terms: -3.058103976 + 4.156444412 = 1.098340436 4.156444412 + -4.077471967t + t2 = 1.098340436 Factor a perfect square on the left side: (t + -2.038735984)(t + -2.038735984) = 1.098340436 Calculate the square root of the right side: 1.048017383 Break this problem into two subproblems by setting (t + -2.038735984) equal to 1.048017383 and -1.048017383.Subproblem 1
t + -2.038735984 = 1.048017383 Simplifying t + -2.038735984 = 1.048017383 Reorder the terms: -2.038735984 + t = 1.048017383 Solving -2.038735984 + t = 1.048017383 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.038735984' to each side of the equation. -2.038735984 + 2.038735984 + t = 1.048017383 + 2.038735984 Combine like terms: -2.038735984 + 2.038735984 = 0.000000000 0.000000000 + t = 1.048017383 + 2.038735984 t = 1.048017383 + 2.038735984 Combine like terms: 1.048017383 + 2.038735984 = 3.086753367 t = 3.086753367 Simplifying t = 3.086753367Subproblem 2
t + -2.038735984 = -1.048017383 Simplifying t + -2.038735984 = -1.048017383 Reorder the terms: -2.038735984 + t = -1.048017383 Solving -2.038735984 + t = -1.048017383 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.038735984' to each side of the equation. -2.038735984 + 2.038735984 + t = -1.048017383 + 2.038735984 Combine like terms: -2.038735984 + 2.038735984 = 0.000000000 0.000000000 + t = -1.048017383 + 2.038735984 t = -1.048017383 + 2.038735984 Combine like terms: -1.048017383 + 2.038735984 = 0.990718601 t = 0.990718601 Simplifying t = 0.990718601Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.086753367, 0.990718601}
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