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Simplifying 0 = 79t + 1.95t2 + -1150 Reorder the terms: 0 = -1150 + 79t + 1.95t2 Solving 0 = -1150 + 79t + 1.95t2 Solving for variable 't'. Combine like terms: 0 + 1150 = 1150 1150 + -79t + -1.95t2 = -1150 + 79t + 1.95t2 + 1150 + -79t + -1.95t2 Reorder the terms: 1150 + -79t + -1.95t2 = -1150 + 1150 + 79t + -79t + 1.95t2 + -1.95t2 Combine like terms: -1150 + 1150 = 0 1150 + -79t + -1.95t2 = 0 + 79t + -79t + 1.95t2 + -1.95t2 1150 + -79t + -1.95t2 = 79t + -79t + 1.95t2 + -1.95t2 Combine like terms: 79t + -79t = 0 1150 + -79t + -1.95t2 = 0 + 1.95t2 + -1.95t2 1150 + -79t + -1.95t2 = 1.95t2 + -1.95t2 Combine like terms: 1.95t2 + -1.95t2 = 0.00 1150 + -79t + -1.95t2 = 0.00 Begin completing the square. Divide all terms by -1.95 the coefficient of the squared term: Divide each side by '-1.95'. -589.7435897 + 40.51282051t + t2 = 0 Move the constant term to the right: Add '589.7435897' to each side of the equation. -589.7435897 + 40.51282051t + 589.7435897 + t2 = 0 + 589.7435897 Reorder the terms: -589.7435897 + 589.7435897 + 40.51282051t + t2 = 0 + 589.7435897 Combine like terms: -589.7435897 + 589.7435897 = 0.0000000 0.0000000 + 40.51282051t + t2 = 0 + 589.7435897 40.51282051t + t2 = 0 + 589.7435897 Combine like terms: 0 + 589.7435897 = 589.7435897 40.51282051t + t2 = 589.7435897 The t term is 40.51282051t. Take half its coefficient (20.25641026). Square it (410.3221566) and add it to both sides. Add '410.3221566' to each side of the equation. 40.51282051t + 410.3221566 + t2 = 589.7435897 + 410.3221566 Reorder the terms: 410.3221566 + 40.51282051t + t2 = 589.7435897 + 410.3221566 Combine like terms: 589.7435897 + 410.3221566 = 1000.0657463 410.3221566 + 40.51282051t + t2 = 1000.0657463 Factor a perfect square on the left side: (t + 20.25641026)(t + 20.25641026) = 1000.0657463 Calculate the square root of the right side: 31.623816125 Break this problem into two subproblems by setting (t + 20.25641026) equal to 31.623816125 and -31.623816125.Subproblem 1
t + 20.25641026 = 31.623816125 Simplifying t + 20.25641026 = 31.623816125 Reorder the terms: 20.25641026 + t = 31.623816125 Solving 20.25641026 + t = 31.623816125 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-20.25641026' to each side of the equation. 20.25641026 + -20.25641026 + t = 31.623816125 + -20.25641026 Combine like terms: 20.25641026 + -20.25641026 = 0.00000000 0.00000000 + t = 31.623816125 + -20.25641026 t = 31.623816125 + -20.25641026 Combine like terms: 31.623816125 + -20.25641026 = 11.367405865 t = 11.367405865 Simplifying t = 11.367405865Subproblem 2
t + 20.25641026 = -31.623816125 Simplifying t + 20.25641026 = -31.623816125 Reorder the terms: 20.25641026 + t = -31.623816125 Solving 20.25641026 + t = -31.623816125 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-20.25641026' to each side of the equation. 20.25641026 + -20.25641026 + t = -31.623816125 + -20.25641026 Combine like terms: 20.25641026 + -20.25641026 = 0.00000000 0.00000000 + t = -31.623816125 + -20.25641026 t = -31.623816125 + -20.25641026 Combine like terms: -31.623816125 + -20.25641026 = -51.880226385 t = -51.880226385 Simplifying t = -51.880226385Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.367405865, -51.880226385}
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