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Simplifying 14t + -4.9t2 + 63 = 0 Reorder the terms: 63 + 14t + -4.9t2 = 0 Solving 63 + 14t + -4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -12.85714286 + -2.857142857t + t2 = 0 Move the constant term to the right: Add '12.85714286' to each side of the equation. -12.85714286 + -2.857142857t + 12.85714286 + t2 = 0 + 12.85714286 Reorder the terms: -12.85714286 + 12.85714286 + -2.857142857t + t2 = 0 + 12.85714286 Combine like terms: -12.85714286 + 12.85714286 = 0.00000000 0.00000000 + -2.857142857t + t2 = 0 + 12.85714286 -2.857142857t + t2 = 0 + 12.85714286 Combine like terms: 0 + 12.85714286 = 12.85714286 -2.857142857t + t2 = 12.85714286 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 = 12.85714286 + 2.040816328 Reorder the terms: 2.040816328 + -2.857142857t + t2 = 12.85714286 + 2.040816328 Combine like terms: 12.85714286 + 2.040816328 = 14.897959188 2.040816328 + -2.857142857t + t2 = 14.897959188 Factor a perfect square on the left side: (t + -1.428571429)(t + -1.428571429) = 14.897959188 Calculate the square root of the right side: 3.859787454 Break this problem into two subproblems by setting (t + -1.428571429) equal to 3.859787454 and -3.859787454.Subproblem 1
t + -1.428571429 = 3.859787454 Simplifying t + -1.428571429 = 3.859787454 Reorder the terms: -1.428571429 + t = 3.859787454 Solving -1.428571429 + t = 3.859787454 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 = 3.859787454 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + t = 3.859787454 + 1.428571429 t = 3.859787454 + 1.428571429 Combine like terms: 3.859787454 + 1.428571429 = 5.288358883 t = 5.288358883 Simplifying t = 5.288358883Subproblem 2
t + -1.428571429 = -3.859787454 Simplifying t + -1.428571429 = -3.859787454 Reorder the terms: -1.428571429 + t = -3.859787454 Solving -1.428571429 + t = -3.859787454 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 = -3.859787454 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + t = -3.859787454 + 1.428571429 t = -3.859787454 + 1.428571429 Combine like terms: -3.859787454 + 1.428571429 = -2.431216025 t = -2.431216025 Simplifying t = -2.431216025Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.288358883, -2.431216025}
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