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Simplifying 55 = t + 4.9t2 Solving 55 = t + 4.9t2 Solving for variable 't'. Reorder the terms: 55 + -1t + -4.9t2 = t + -1t + 4.9t2 + -4.9t2 Combine like terms: t + -1t = 0 55 + -1t + -4.9t2 = 0 + 4.9t2 + -4.9t2 55 + -1t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 55 + -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'. -11.2244898 + 0.2040816327t + t2 = 0 Move the constant term to the right: Add '11.2244898' to each side of the equation. -11.2244898 + 0.2040816327t + 11.2244898 + t2 = 0 + 11.2244898 Reorder the terms: -11.2244898 + 11.2244898 + 0.2040816327t + t2 = 0 + 11.2244898 Combine like terms: -11.2244898 + 11.2244898 = 0.0000000 0.0000000 + 0.2040816327t + t2 = 0 + 11.2244898 0.2040816327t + t2 = 0 + 11.2244898 Combine like terms: 0 + 11.2244898 = 11.2244898 0.2040816327t + t2 = 11.2244898 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 = 11.2244898 + 0.01041232821 Reorder the terms: 0.01041232821 + 0.2040816327t + t2 = 11.2244898 + 0.01041232821 Combine like terms: 11.2244898 + 0.01041232821 = 11.23490212821 0.01041232821 + 0.2040816327t + t2 = 11.23490212821 Factor a perfect square on the left side: (t + 0.1020408164)(t + 0.1020408164) = 11.23490212821 Calculate the square root of the right side: 3.351850553 Break this problem into two subproblems by setting (t + 0.1020408164) equal to 3.351850553 and -3.351850553.Subproblem 1
t + 0.1020408164 = 3.351850553 Simplifying t + 0.1020408164 = 3.351850553 Reorder the terms: 0.1020408164 + t = 3.351850553 Solving 0.1020408164 + t = 3.351850553 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 = 3.351850553 + -0.1020408164 Combine like terms: 0.1020408164 + -0.1020408164 = 0.0000000000 0.0000000000 + t = 3.351850553 + -0.1020408164 t = 3.351850553 + -0.1020408164 Combine like terms: 3.351850553 + -0.1020408164 = 3.2498097366 t = 3.2498097366 Simplifying t = 3.2498097366Subproblem 2
t + 0.1020408164 = -3.351850553 Simplifying t + 0.1020408164 = -3.351850553 Reorder the terms: 0.1020408164 + t = -3.351850553 Solving 0.1020408164 + t = -3.351850553 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 = -3.351850553 + -0.1020408164 Combine like terms: 0.1020408164 + -0.1020408164 = 0.0000000000 0.0000000000 + t = -3.351850553 + -0.1020408164 t = -3.351850553 + -0.1020408164 Combine like terms: -3.351850553 + -0.1020408164 = -3.4538913694 t = -3.4538913694 Simplifying t = -3.4538913694Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.2498097366, -3.4538913694}
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