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Simplifying 100 = -19.97t + 4.9t2 Solving 100 = -19.97t + 4.9t2 Solving for variable 't'. Reorder the terms: 100 + 19.97t + -4.9t2 = -19.97t + 19.97t + 4.9t2 + -4.9t2 Combine like terms: -19.97t + 19.97t = 0.00 100 + 19.97t + -4.9t2 = 0.00 + 4.9t2 + -4.9t2 100 + 19.97t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 100 + 19.97t + -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'. -20.40816327 + -4.075510204t + t2 = 0 Move the constant term to the right: Add '20.40816327' to each side of the equation. -20.40816327 + -4.075510204t + 20.40816327 + t2 = 0 + 20.40816327 Reorder the terms: -20.40816327 + 20.40816327 + -4.075510204t + t2 = 0 + 20.40816327 Combine like terms: -20.40816327 + 20.40816327 = 0.00000000 0.00000000 + -4.075510204t + t2 = 0 + 20.40816327 -4.075510204t + t2 = 0 + 20.40816327 Combine like terms: 0 + 20.40816327 = 20.40816327 -4.075510204t + t2 = 20.40816327 The t term is -4.075510204t. Take half its coefficient (-2.037755102). Square it (4.152445856) and add it to both sides. Add '4.152445856' to each side of the equation. -4.075510204t + 4.152445856 + t2 = 20.40816327 + 4.152445856 Reorder the terms: 4.152445856 + -4.075510204t + t2 = 20.40816327 + 4.152445856 Combine like terms: 20.40816327 + 4.152445856 = 24.560609126 4.152445856 + -4.075510204t + t2 = 24.560609126 Factor a perfect square on the left side: (t + -2.037755102)(t + -2.037755102) = 24.560609126 Calculate the square root of the right side: 4.955866133 Break this problem into two subproblems by setting (t + -2.037755102) equal to 4.955866133 and -4.955866133.Subproblem 1
t + -2.037755102 = 4.955866133 Simplifying t + -2.037755102 = 4.955866133 Reorder the terms: -2.037755102 + t = 4.955866133 Solving -2.037755102 + t = 4.955866133 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.037755102' to each side of the equation. -2.037755102 + 2.037755102 + t = 4.955866133 + 2.037755102 Combine like terms: -2.037755102 + 2.037755102 = 0.000000000 0.000000000 + t = 4.955866133 + 2.037755102 t = 4.955866133 + 2.037755102 Combine like terms: 4.955866133 + 2.037755102 = 6.993621235 t = 6.993621235 Simplifying t = 6.993621235Subproblem 2
t + -2.037755102 = -4.955866133 Simplifying t + -2.037755102 = -4.955866133 Reorder the terms: -2.037755102 + t = -4.955866133 Solving -2.037755102 + t = -4.955866133 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.037755102' to each side of the equation. -2.037755102 + 2.037755102 + t = -4.955866133 + 2.037755102 Combine like terms: -2.037755102 + 2.037755102 = 0.000000000 0.000000000 + t = -4.955866133 + 2.037755102 t = -4.955866133 + 2.037755102 Combine like terms: -4.955866133 + 2.037755102 = -2.918111031 t = -2.918111031 Simplifying t = -2.918111031Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.993621235, -2.918111031}
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