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Simplifying 4.9t2 + -10t + -92 = 0 Reorder the terms: -92 + -10t + 4.9t2 = 0 Solving -92 + -10t + 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'. -18.7755102 + -2.040816327t + t2 = 0 Move the constant term to the right: Add '18.7755102' to each side of the equation. -18.7755102 + -2.040816327t + 18.7755102 + t2 = 0 + 18.7755102 Reorder the terms: -18.7755102 + 18.7755102 + -2.040816327t + t2 = 0 + 18.7755102 Combine like terms: -18.7755102 + 18.7755102 = 0.0000000 0.0000000 + -2.040816327t + t2 = 0 + 18.7755102 -2.040816327t + t2 = 0 + 18.7755102 Combine like terms: 0 + 18.7755102 = 18.7755102 -2.040816327t + t2 = 18.7755102 The t term is -2.040816327t. Take half its coefficient (-1.020408164). Square it (1.041232821) and add it to both sides. Add '1.041232821' to each side of the equation. -2.040816327t + 1.041232821 + t2 = 18.7755102 + 1.041232821 Reorder the terms: 1.041232821 + -2.040816327t + t2 = 18.7755102 + 1.041232821 Combine like terms: 18.7755102 + 1.041232821 = 19.816743021 1.041232821 + -2.040816327t + t2 = 19.816743021 Factor a perfect square on the left side: (t + -1.020408164)(t + -1.020408164) = 19.816743021 Calculate the square root of the right side: 4.451600052 Break this problem into two subproblems by setting (t + -1.020408164) equal to 4.451600052 and -4.451600052.Subproblem 1
t + -1.020408164 = 4.451600052 Simplifying t + -1.020408164 = 4.451600052 Reorder the terms: -1.020408164 + t = 4.451600052 Solving -1.020408164 + t = 4.451600052 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.020408164' to each side of the equation. -1.020408164 + 1.020408164 + t = 4.451600052 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + t = 4.451600052 + 1.020408164 t = 4.451600052 + 1.020408164 Combine like terms: 4.451600052 + 1.020408164 = 5.472008216 t = 5.472008216 Simplifying t = 5.472008216Subproblem 2
t + -1.020408164 = -4.451600052 Simplifying t + -1.020408164 = -4.451600052 Reorder the terms: -1.020408164 + t = -4.451600052 Solving -1.020408164 + t = -4.451600052 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.020408164' to each side of the equation. -1.020408164 + 1.020408164 + t = -4.451600052 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + t = -4.451600052 + 1.020408164 t = -4.451600052 + 1.020408164 Combine like terms: -4.451600052 + 1.020408164 = -3.431191888 t = -3.431191888 Simplifying t = -3.431191888Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.472008216, -3.431191888}
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