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Simplifying 0 = 74 + 11.4t + -4.9t2 Solving 0 = 74 + 11.4t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -74 = -74 -74 + -11.4t + 4.9t2 = 74 + 11.4t + -4.9t2 + -74 + -11.4t + 4.9t2 Reorder the terms: -74 + -11.4t + 4.9t2 = 74 + -74 + 11.4t + -11.4t + -4.9t2 + 4.9t2 Combine like terms: 74 + -74 = 0 -74 + -11.4t + 4.9t2 = 0 + 11.4t + -11.4t + -4.9t2 + 4.9t2 -74 + -11.4t + 4.9t2 = 11.4t + -11.4t + -4.9t2 + 4.9t2 Combine like terms: 11.4t + -11.4t = 0.0 -74 + -11.4t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 -74 + -11.4t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -74 + -11.4t + 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'. -15.10204082 + -2.326530612t + t2 = 0 Move the constant term to the right: Add '15.10204082' to each side of the equation. -15.10204082 + -2.326530612t + 15.10204082 + t2 = 0 + 15.10204082 Reorder the terms: -15.10204082 + 15.10204082 + -2.326530612t + t2 = 0 + 15.10204082 Combine like terms: -15.10204082 + 15.10204082 = 0.00000000 0.00000000 + -2.326530612t + t2 = 0 + 15.10204082 -2.326530612t + t2 = 0 + 15.10204082 Combine like terms: 0 + 15.10204082 = 15.10204082 -2.326530612t + t2 = 15.10204082 The t term is -2.326530612t. Take half its coefficient (-1.163265306). Square it (1.353186172) and add it to both sides. Add '1.353186172' to each side of the equation. -2.326530612t + 1.353186172 + t2 = 15.10204082 + 1.353186172 Reorder the terms: 1.353186172 + -2.326530612t + t2 = 15.10204082 + 1.353186172 Combine like terms: 15.10204082 + 1.353186172 = 16.455226992 1.353186172 + -2.326530612t + t2 = 16.455226992 Factor a perfect square on the left side: (t + -1.163265306)(t + -1.163265306) = 16.455226992 Calculate the square root of the right side: 4.056504282 Break this problem into two subproblems by setting (t + -1.163265306) equal to 4.056504282 and -4.056504282.Subproblem 1
t + -1.163265306 = 4.056504282 Simplifying t + -1.163265306 = 4.056504282 Reorder the terms: -1.163265306 + t = 4.056504282 Solving -1.163265306 + t = 4.056504282 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.163265306' to each side of the equation. -1.163265306 + 1.163265306 + t = 4.056504282 + 1.163265306 Combine like terms: -1.163265306 + 1.163265306 = 0.000000000 0.000000000 + t = 4.056504282 + 1.163265306 t = 4.056504282 + 1.163265306 Combine like terms: 4.056504282 + 1.163265306 = 5.219769588 t = 5.219769588 Simplifying t = 5.219769588Subproblem 2
t + -1.163265306 = -4.056504282 Simplifying t + -1.163265306 = -4.056504282 Reorder the terms: -1.163265306 + t = -4.056504282 Solving -1.163265306 + t = -4.056504282 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.163265306' to each side of the equation. -1.163265306 + 1.163265306 + t = -4.056504282 + 1.163265306 Combine like terms: -1.163265306 + 1.163265306 = 0.000000000 0.000000000 + t = -4.056504282 + 1.163265306 t = -4.056504282 + 1.163265306 Combine like terms: -4.056504282 + 1.163265306 = -2.893238976 t = -2.893238976 Simplifying t = -2.893238976Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.219769588, -2.893238976}
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