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Simplifying 0 = -4.9t2 + 14t + 3 Reorder the terms: 0 = 3 + 14t + -4.9t2 Solving 0 = 3 + 14t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -3 = -3 -3 + -14t + 4.9t2 = 3 + 14t + -4.9t2 + -3 + -14t + 4.9t2 Reorder the terms: -3 + -14t + 4.9t2 = 3 + -3 + 14t + -14t + -4.9t2 + 4.9t2 Combine like terms: 3 + -3 = 0 -3 + -14t + 4.9t2 = 0 + 14t + -14t + -4.9t2 + 4.9t2 -3 + -14t + 4.9t2 = 14t + -14t + -4.9t2 + 4.9t2 Combine like terms: 14t + -14t = 0 -3 + -14t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -3 + -14t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -3 + -14t + 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'. -0.612244898 + -2.857142857t + t2 = 0 Move the constant term to the right: Add '0.612244898' to each side of the equation. -0.612244898 + -2.857142857t + 0.612244898 + t2 = 0 + 0.612244898 Reorder the terms: -0.612244898 + 0.612244898 + -2.857142857t + t2 = 0 + 0.612244898 Combine like terms: -0.612244898 + 0.612244898 = 0.000000000 0.000000000 + -2.857142857t + t2 = 0 + 0.612244898 -2.857142857t + t2 = 0 + 0.612244898 Combine like terms: 0 + 0.612244898 = 0.612244898 -2.857142857t + t2 = 0.612244898 The t term is -2.857142857t. Take half its coefficient (-1.428571429). Square it (2.040816328) and add it to both sides. Add '2.040816328' to each side of the equation. -2.857142857t + 2.040816328 + t2 = 0.612244898 + 2.040816328 Reorder the terms: 2.040816328 + -2.857142857t + t2 = 0.612244898 + 2.040816328 Combine like terms: 0.612244898 + 2.040816328 = 2.653061226 2.040816328 + -2.857142857t + t2 = 2.653061226 Factor a perfect square on the left side: (t + -1.428571429)(t + -1.428571429) = 2.653061226 Calculate the square root of the right side: 1.628822036 Break this problem into two subproblems by setting (t + -1.428571429) equal to 1.628822036 and -1.628822036.Subproblem 1
t + -1.428571429 = 1.628822036 Simplifying t + -1.428571429 = 1.628822036 Reorder the terms: -1.428571429 + t = 1.628822036 Solving -1.428571429 + t = 1.628822036 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + t = 1.628822036 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + t = 1.628822036 + 1.428571429 t = 1.628822036 + 1.428571429 Combine like terms: 1.628822036 + 1.428571429 = 3.057393465 t = 3.057393465 Simplifying t = 3.057393465Subproblem 2
t + -1.428571429 = -1.628822036 Simplifying t + -1.428571429 = -1.628822036 Reorder the terms: -1.428571429 + t = -1.628822036 Solving -1.428571429 + t = -1.628822036 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + t = -1.628822036 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + t = -1.628822036 + 1.428571429 t = -1.628822036 + 1.428571429 Combine like terms: -1.628822036 + 1.428571429 = -0.200250607 t = -0.200250607 Simplifying t = -0.200250607Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.057393465, -0.200250607}
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