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Simplifying 0 = 4.9t2 + -14t + 2 Reorder the terms: 0 = 2 + -14t + 4.9t2 Solving 0 = 2 + -14t + 4.9t2 Solving for variable 't'. Combine like terms: 0 + -2 = -2 -2 + 14t + -4.9t2 = 2 + -14t + 4.9t2 + -2 + 14t + -4.9t2 Reorder the terms: -2 + 14t + -4.9t2 = 2 + -2 + -14t + 14t + 4.9t2 + -4.9t2 Combine like terms: 2 + -2 = 0 -2 + 14t + -4.9t2 = 0 + -14t + 14t + 4.9t2 + -4.9t2 -2 + 14t + -4.9t2 = -14t + 14t + 4.9t2 + -4.9t2 Combine like terms: -14t + 14t = 0 -2 + 14t + -4.9t2 = 0 + 4.9t2 + -4.9t2 -2 + 14t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 -2 + 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'. 0.4081632653 + -2.857142857t + t2 = 0 Move the constant term to the right: Add '-0.4081632653' to each side of the equation. 0.4081632653 + -2.857142857t + -0.4081632653 + t2 = 0 + -0.4081632653 Reorder the terms: 0.4081632653 + -0.4081632653 + -2.857142857t + t2 = 0 + -0.4081632653 Combine like terms: 0.4081632653 + -0.4081632653 = 0.0000000000 0.0000000000 + -2.857142857t + t2 = 0 + -0.4081632653 -2.857142857t + t2 = 0 + -0.4081632653 Combine like terms: 0 + -0.4081632653 = -0.4081632653 -2.857142857t + t2 = -0.4081632653 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 = -0.4081632653 + 2.040816328 Reorder the terms: 2.040816328 + -2.857142857t + t2 = -0.4081632653 + 2.040816328 Combine like terms: -0.4081632653 + 2.040816328 = 1.6326530627 2.040816328 + -2.857142857t + t2 = 1.6326530627 Factor a perfect square on the left side: (t + -1.428571429)(t + -1.428571429) = 1.6326530627 Calculate the square root of the right side: 1.277753131 Break this problem into two subproblems by setting (t + -1.428571429) equal to 1.277753131 and -1.277753131.Subproblem 1
t + -1.428571429 = 1.277753131 Simplifying t + -1.428571429 = 1.277753131 Reorder the terms: -1.428571429 + t = 1.277753131 Solving -1.428571429 + t = 1.277753131 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 = 1.277753131 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + t = 1.277753131 + 1.428571429 t = 1.277753131 + 1.428571429 Combine like terms: 1.277753131 + 1.428571429 = 2.70632456 t = 2.70632456 Simplifying t = 2.70632456Subproblem 2
t + -1.428571429 = -1.277753131 Simplifying t + -1.428571429 = -1.277753131 Reorder the terms: -1.428571429 + t = -1.277753131 Solving -1.428571429 + t = -1.277753131 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 = -1.277753131 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + t = -1.277753131 + 1.428571429 t = -1.277753131 + 1.428571429 Combine like terms: -1.277753131 + 1.428571429 = 0.150818298 t = 0.150818298 Simplifying t = 0.150818298Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.70632456, 0.150818298}
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