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Simplifying -4.9t2 + 10t + 190 = 0 Reorder the terms: 190 + 10t + -4.9t2 = 0 Solving 190 + 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'. -38.7755102 + -2.040816327t + t2 = 0 Move the constant term to the right: Add '38.7755102' to each side of the equation. -38.7755102 + -2.040816327t + 38.7755102 + t2 = 0 + 38.7755102 Reorder the terms: -38.7755102 + 38.7755102 + -2.040816327t + t2 = 0 + 38.7755102 Combine like terms: -38.7755102 + 38.7755102 = 0.0000000 0.0000000 + -2.040816327t + t2 = 0 + 38.7755102 -2.040816327t + t2 = 0 + 38.7755102 Combine like terms: 0 + 38.7755102 = 38.7755102 -2.040816327t + t2 = 38.7755102 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 = 38.7755102 + 1.041232821 Reorder the terms: 1.041232821 + -2.040816327t + t2 = 38.7755102 + 1.041232821 Combine like terms: 38.7755102 + 1.041232821 = 39.816743021 1.041232821 + -2.040816327t + t2 = 39.816743021 Factor a perfect square on the left side: (t + -1.020408164)(t + -1.020408164) = 39.816743021 Calculate the square root of the right side: 6.310050952 Break this problem into two subproblems by setting (t + -1.020408164) equal to 6.310050952 and -6.310050952.Subproblem 1
t + -1.020408164 = 6.310050952 Simplifying t + -1.020408164 = 6.310050952 Reorder the terms: -1.020408164 + t = 6.310050952 Solving -1.020408164 + t = 6.310050952 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 = 6.310050952 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + t = 6.310050952 + 1.020408164 t = 6.310050952 + 1.020408164 Combine like terms: 6.310050952 + 1.020408164 = 7.330459116 t = 7.330459116 Simplifying t = 7.330459116Subproblem 2
t + -1.020408164 = -6.310050952 Simplifying t + -1.020408164 = -6.310050952 Reorder the terms: -1.020408164 + t = -6.310050952 Solving -1.020408164 + t = -6.310050952 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 = -6.310050952 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + t = -6.310050952 + 1.020408164 t = -6.310050952 + 1.020408164 Combine like terms: -6.310050952 + 1.020408164 = -5.289642788 t = -5.289642788 Simplifying t = -5.289642788Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.330459116, -5.289642788}
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