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Simplifying 0 = 4.9t2 + -30t + 10 Reorder the terms: 0 = 10 + -30t + 4.9t2 Solving 0 = 10 + -30t + 4.9t2 Solving for variable 't'. Combine like terms: 0 + -10 = -10 -10 + 30t + -4.9t2 = 10 + -30t + 4.9t2 + -10 + 30t + -4.9t2 Reorder the terms: -10 + 30t + -4.9t2 = 10 + -10 + -30t + 30t + 4.9t2 + -4.9t2 Combine like terms: 10 + -10 = 0 -10 + 30t + -4.9t2 = 0 + -30t + 30t + 4.9t2 + -4.9t2 -10 + 30t + -4.9t2 = -30t + 30t + 4.9t2 + -4.9t2 Combine like terms: -30t + 30t = 0 -10 + 30t + -4.9t2 = 0 + 4.9t2 + -4.9t2 -10 + 30t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 -10 + 30t + -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'. 2.040816327 + -6.12244898t + t2 = 0 Move the constant term to the right: Add '-2.040816327' to each side of the equation. 2.040816327 + -6.12244898t + -2.040816327 + t2 = 0 + -2.040816327 Reorder the terms: 2.040816327 + -2.040816327 + -6.12244898t + t2 = 0 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + -6.12244898t + t2 = 0 + -2.040816327 -6.12244898t + t2 = 0 + -2.040816327 Combine like terms: 0 + -2.040816327 = -2.040816327 -6.12244898t + t2 = -2.040816327 The t term is -6.12244898t. Take half its coefficient (-3.06122449). Square it (9.371095378) and add it to both sides. Add '9.371095378' to each side of the equation. -6.12244898t + 9.371095378 + t2 = -2.040816327 + 9.371095378 Reorder the terms: 9.371095378 + -6.12244898t + t2 = -2.040816327 + 9.371095378 Combine like terms: -2.040816327 + 9.371095378 = 7.330279051 9.371095378 + -6.12244898t + t2 = 7.330279051 Factor a perfect square on the left side: (t + -3.06122449)(t + -3.06122449) = 7.330279051 Calculate the square root of the right side: 2.707448809 Break this problem into two subproblems by setting (t + -3.06122449) equal to 2.707448809 and -2.707448809.Subproblem 1
t + -3.06122449 = 2.707448809 Simplifying t + -3.06122449 = 2.707448809 Reorder the terms: -3.06122449 + t = 2.707448809 Solving -3.06122449 + t = 2.707448809 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.06122449' to each side of the equation. -3.06122449 + 3.06122449 + t = 2.707448809 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + t = 2.707448809 + 3.06122449 t = 2.707448809 + 3.06122449 Combine like terms: 2.707448809 + 3.06122449 = 5.768673299 t = 5.768673299 Simplifying t = 5.768673299Subproblem 2
t + -3.06122449 = -2.707448809 Simplifying t + -3.06122449 = -2.707448809 Reorder the terms: -3.06122449 + t = -2.707448809 Solving -3.06122449 + t = -2.707448809 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.06122449' to each side of the equation. -3.06122449 + 3.06122449 + t = -2.707448809 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + t = -2.707448809 + 3.06122449 t = -2.707448809 + 3.06122449 Combine like terms: -2.707448809 + 3.06122449 = 0.353775681 t = 0.353775681 Simplifying t = 0.353775681Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.768673299, 0.353775681}
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