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Simplifying 0 = 4.9t2 + 15t + -92 Reorder the terms: 0 = -92 + 15t + 4.9t2 Solving 0 = -92 + 15t + 4.9t2 Solving for variable 't'. Combine like terms: 0 + 92 = 92 92 + -15t + -4.9t2 = -92 + 15t + 4.9t2 + 92 + -15t + -4.9t2 Reorder the terms: 92 + -15t + -4.9t2 = -92 + 92 + 15t + -15t + 4.9t2 + -4.9t2 Combine like terms: -92 + 92 = 0 92 + -15t + -4.9t2 = 0 + 15t + -15t + 4.9t2 + -4.9t2 92 + -15t + -4.9t2 = 15t + -15t + 4.9t2 + -4.9t2 Combine like terms: 15t + -15t = 0 92 + -15t + -4.9t2 = 0 + 4.9t2 + -4.9t2 92 + -15t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 92 + -15t + -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'. -18.7755102 + 3.06122449t + t2 = 0 Move the constant term to the right: Add '18.7755102' to each side of the equation. -18.7755102 + 3.06122449t + 18.7755102 + t2 = 0 + 18.7755102 Reorder the terms: -18.7755102 + 18.7755102 + 3.06122449t + t2 = 0 + 18.7755102 Combine like terms: -18.7755102 + 18.7755102 = 0.0000000 0.0000000 + 3.06122449t + t2 = 0 + 18.7755102 3.06122449t + t2 = 0 + 18.7755102 Combine like terms: 0 + 18.7755102 = 18.7755102 3.06122449t + t2 = 18.7755102 The t term is 3.06122449t. Take half its coefficient (1.530612245). Square it (2.342773845) and add it to both sides. Add '2.342773845' to each side of the equation. 3.06122449t + 2.342773845 + t2 = 18.7755102 + 2.342773845 Reorder the terms: 2.342773845 + 3.06122449t + t2 = 18.7755102 + 2.342773845 Combine like terms: 18.7755102 + 2.342773845 = 21.118284045 2.342773845 + 3.06122449t + t2 = 21.118284045 Factor a perfect square on the left side: (t + 1.530612245)(t + 1.530612245) = 21.118284045 Calculate the square root of the right side: 4.59546342 Break this problem into two subproblems by setting (t + 1.530612245) equal to 4.59546342 and -4.59546342.Subproblem 1
t + 1.530612245 = 4.59546342 Simplifying t + 1.530612245 = 4.59546342 Reorder the terms: 1.530612245 + t = 4.59546342 Solving 1.530612245 + t = 4.59546342 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.530612245' to each side of the equation. 1.530612245 + -1.530612245 + t = 4.59546342 + -1.530612245 Combine like terms: 1.530612245 + -1.530612245 = 0.000000000 0.000000000 + t = 4.59546342 + -1.530612245 t = 4.59546342 + -1.530612245 Combine like terms: 4.59546342 + -1.530612245 = 3.064851175 t = 3.064851175 Simplifying t = 3.064851175Subproblem 2
t + 1.530612245 = -4.59546342 Simplifying t + 1.530612245 = -4.59546342 Reorder the terms: 1.530612245 + t = -4.59546342 Solving 1.530612245 + t = -4.59546342 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.530612245' to each side of the equation. 1.530612245 + -1.530612245 + t = -4.59546342 + -1.530612245 Combine like terms: 1.530612245 + -1.530612245 = 0.000000000 0.000000000 + t = -4.59546342 + -1.530612245 t = -4.59546342 + -1.530612245 Combine like terms: -4.59546342 + -1.530612245 = -6.126075665 t = -6.126075665 Simplifying t = -6.126075665Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.064851175, -6.126075665}
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