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Simplifying 0 = -1.85t2 + 30t + 6 Reorder the terms: 0 = 6 + 30t + -1.85t2 Solving 0 = 6 + 30t + -1.85t2 Solving for variable 't'. Combine like terms: 0 + -6 = -6 -6 + -30t + 1.85t2 = 6 + 30t + -1.85t2 + -6 + -30t + 1.85t2 Reorder the terms: -6 + -30t + 1.85t2 = 6 + -6 + 30t + -30t + -1.85t2 + 1.85t2 Combine like terms: 6 + -6 = 0 -6 + -30t + 1.85t2 = 0 + 30t + -30t + -1.85t2 + 1.85t2 -6 + -30t + 1.85t2 = 30t + -30t + -1.85t2 + 1.85t2 Combine like terms: 30t + -30t = 0 -6 + -30t + 1.85t2 = 0 + -1.85t2 + 1.85t2 -6 + -30t + 1.85t2 = -1.85t2 + 1.85t2 Combine like terms: -1.85t2 + 1.85t2 = 0.00 -6 + -30t + 1.85t2 = 0.00 Begin completing the square. Divide all terms by 1.85 the coefficient of the squared term: Divide each side by '1.85'. -3.243243243 + -16.21621622t + t2 = 0 Move the constant term to the right: Add '3.243243243' to each side of the equation. -3.243243243 + -16.21621622t + 3.243243243 + t2 = 0 + 3.243243243 Reorder the terms: -3.243243243 + 3.243243243 + -16.21621622t + t2 = 0 + 3.243243243 Combine like terms: -3.243243243 + 3.243243243 = 0.000000000 0.000000000 + -16.21621622t + t2 = 0 + 3.243243243 -16.21621622t + t2 = 0 + 3.243243243 Combine like terms: 0 + 3.243243243 = 3.243243243 -16.21621622t + t2 = 3.243243243 The t term is -16.21621622t. Take half its coefficient (-8.10810811). Square it (65.74141712) and add it to both sides. Add '65.74141712' to each side of the equation. -16.21621622t + 65.74141712 + t2 = 3.243243243 + 65.74141712 Reorder the terms: 65.74141712 + -16.21621622t + t2 = 3.243243243 + 65.74141712 Combine like terms: 3.243243243 + 65.74141712 = 68.984660363 65.74141712 + -16.21621622t + t2 = 68.984660363 Factor a perfect square on the left side: (t + -8.10810811)(t + -8.10810811) = 68.984660363 Calculate the square root of the right side: 8.305700474 Break this problem into two subproblems by setting (t + -8.10810811) equal to 8.305700474 and -8.305700474.Subproblem 1
t + -8.10810811 = 8.305700474 Simplifying t + -8.10810811 = 8.305700474 Reorder the terms: -8.10810811 + t = 8.305700474 Solving -8.10810811 + t = 8.305700474 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '8.10810811' to each side of the equation. -8.10810811 + 8.10810811 + t = 8.305700474 + 8.10810811 Combine like terms: -8.10810811 + 8.10810811 = 0.00000000 0.00000000 + t = 8.305700474 + 8.10810811 t = 8.305700474 + 8.10810811 Combine like terms: 8.305700474 + 8.10810811 = 16.413808584 t = 16.413808584 Simplifying t = 16.413808584Subproblem 2
t + -8.10810811 = -8.305700474 Simplifying t + -8.10810811 = -8.305700474 Reorder the terms: -8.10810811 + t = -8.305700474 Solving -8.10810811 + t = -8.305700474 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '8.10810811' to each side of the equation. -8.10810811 + 8.10810811 + t = -8.305700474 + 8.10810811 Combine like terms: -8.10810811 + 8.10810811 = 0.00000000 0.00000000 + t = -8.305700474 + 8.10810811 t = -8.305700474 + 8.10810811 Combine like terms: -8.305700474 + 8.10810811 = -0.197592364 t = -0.197592364 Simplifying t = -0.197592364Solution
The solution to the problem is based on the solutions from the subproblems. t = {16.413808584, -0.197592364}
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