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Simplifying 2.7 = -2.9t + 9.8t2 Solving 2.7 = -2.9t + 9.8t2 Solving for variable 't'. Reorder the terms: 2.7 + 2.9t + -9.8t2 = -2.9t + 2.9t + 9.8t2 + -9.8t2 Combine like terms: -2.9t + 2.9t = 0.0 2.7 + 2.9t + -9.8t2 = 0.0 + 9.8t2 + -9.8t2 2.7 + 2.9t + -9.8t2 = 9.8t2 + -9.8t2 Combine like terms: 9.8t2 + -9.8t2 = 0.0 2.7 + 2.9t + -9.8t2 = 0.0 Begin completing the square. Divide all terms by -9.8 the coefficient of the squared term: Divide each side by '-9.8'. -0.2755102041 + -0.2959183673t + t2 = 0 Move the constant term to the right: Add '0.2755102041' to each side of the equation. -0.2755102041 + -0.2959183673t + 0.2755102041 + t2 = 0 + 0.2755102041 Reorder the terms: -0.2755102041 + 0.2755102041 + -0.2959183673t + t2 = 0 + 0.2755102041 Combine like terms: -0.2755102041 + 0.2755102041 = 0.0000000000 0.0000000000 + -0.2959183673t + t2 = 0 + 0.2755102041 -0.2959183673t + t2 = 0 + 0.2755102041 Combine like terms: 0 + 0.2755102041 = 0.2755102041 -0.2959183673t + t2 = 0.2755102041 The t term is -0.2959183673t. Take half its coefficient (-0.1479591837). Square it (0.02189192004) and add it to both sides. Add '0.02189192004' to each side of the equation. -0.2959183673t + 0.02189192004 + t2 = 0.2755102041 + 0.02189192004 Reorder the terms: 0.02189192004 + -0.2959183673t + t2 = 0.2755102041 + 0.02189192004 Combine like terms: 0.2755102041 + 0.02189192004 = 0.29740212414 0.02189192004 + -0.2959183673t + t2 = 0.29740212414 Factor a perfect square on the left side: (t + -0.1479591837)(t + -0.1479591837) = 0.29740212414 Calculate the square root of the right side: 0.545345876 Break this problem into two subproblems by setting (t + -0.1479591837) equal to 0.545345876 and -0.545345876.Subproblem 1
t + -0.1479591837 = 0.545345876 Simplifying t + -0.1479591837 = 0.545345876 Reorder the terms: -0.1479591837 + t = 0.545345876 Solving -0.1479591837 + t = 0.545345876 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1479591837' to each side of the equation. -0.1479591837 + 0.1479591837 + t = 0.545345876 + 0.1479591837 Combine like terms: -0.1479591837 + 0.1479591837 = 0.0000000000 0.0000000000 + t = 0.545345876 + 0.1479591837 t = 0.545345876 + 0.1479591837 Combine like terms: 0.545345876 + 0.1479591837 = 0.6933050597 t = 0.6933050597 Simplifying t = 0.6933050597Subproblem 2
t + -0.1479591837 = -0.545345876 Simplifying t + -0.1479591837 = -0.545345876 Reorder the terms: -0.1479591837 + t = -0.545345876 Solving -0.1479591837 + t = -0.545345876 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1479591837' to each side of the equation. -0.1479591837 + 0.1479591837 + t = -0.545345876 + 0.1479591837 Combine like terms: -0.1479591837 + 0.1479591837 = 0.0000000000 0.0000000000 + t = -0.545345876 + 0.1479591837 t = -0.545345876 + 0.1479591837 Combine like terms: -0.545345876 + 0.1479591837 = -0.3973866923 t = -0.3973866923 Simplifying t = -0.3973866923Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.6933050597, -0.3973866923}
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