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Simplifying 54.6 = 4.9t2 + t Reorder the terms: 54.6 = t + 4.9t2 Solving 54.6 = t + 4.9t2 Solving for variable 't'. Reorder the terms: 54.6 + -1t + -4.9t2 = t + -1t + 4.9t2 + -4.9t2 Combine like terms: t + -1t = 0 54.6 + -1t + -4.9t2 = 0 + 4.9t2 + -4.9t2 54.6 + -1t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 54.6 + -1t + -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'. -11.14285714 + 0.2040816327t + t2 = 0 Move the constant term to the right: Add '11.14285714' to each side of the equation. -11.14285714 + 0.2040816327t + 11.14285714 + t2 = 0 + 11.14285714 Reorder the terms: -11.14285714 + 11.14285714 + 0.2040816327t + t2 = 0 + 11.14285714 Combine like terms: -11.14285714 + 11.14285714 = 0.00000000 0.00000000 + 0.2040816327t + t2 = 0 + 11.14285714 0.2040816327t + t2 = 0 + 11.14285714 Combine like terms: 0 + 11.14285714 = 11.14285714 0.2040816327t + t2 = 11.14285714 The t term is 0.2040816327t. Take half its coefficient (0.1020408164). Square it (0.01041232821) and add it to both sides. Add '0.01041232821' to each side of the equation. 0.2040816327t + 0.01041232821 + t2 = 11.14285714 + 0.01041232821 Reorder the terms: 0.01041232821 + 0.2040816327t + t2 = 11.14285714 + 0.01041232821 Combine like terms: 11.14285714 + 0.01041232821 = 11.15326946821 0.01041232821 + 0.2040816327t + t2 = 11.15326946821 Factor a perfect square on the left side: (t + 0.1020408164)(t + 0.1020408164) = 11.15326946821 Calculate the square root of the right side: 3.3396511 Break this problem into two subproblems by setting (t + 0.1020408164) equal to 3.3396511 and -3.3396511.Subproblem 1
t + 0.1020408164 = 3.3396511 Simplifying t + 0.1020408164 = 3.3396511 Reorder the terms: 0.1020408164 + t = 3.3396511 Solving 0.1020408164 + t = 3.3396511 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.1020408164' to each side of the equation. 0.1020408164 + -0.1020408164 + t = 3.3396511 + -0.1020408164 Combine like terms: 0.1020408164 + -0.1020408164 = 0.0000000000 0.0000000000 + t = 3.3396511 + -0.1020408164 t = 3.3396511 + -0.1020408164 Combine like terms: 3.3396511 + -0.1020408164 = 3.2376102836 t = 3.2376102836 Simplifying t = 3.2376102836Subproblem 2
t + 0.1020408164 = -3.3396511 Simplifying t + 0.1020408164 = -3.3396511 Reorder the terms: 0.1020408164 + t = -3.3396511 Solving 0.1020408164 + t = -3.3396511 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.1020408164' to each side of the equation. 0.1020408164 + -0.1020408164 + t = -3.3396511 + -0.1020408164 Combine like terms: 0.1020408164 + -0.1020408164 = 0.0000000000 0.0000000000 + t = -3.3396511 + -0.1020408164 t = -3.3396511 + -0.1020408164 Combine like terms: -3.3396511 + -0.1020408164 = -3.4416919164 t = -3.4416919164 Simplifying t = -3.4416919164Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.2376102836, -3.4416919164}
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