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Simplifying 4.9t2 + -1(4.2104 * 0.259t) + -0.28 = 0 Multiply 4.2104 * 0.259 4.9t2 + -1(1.0904936t) + -0.28 = 0 Remove parenthesis around (1.0904936t) 4.9t2 + -1 * 1.0904936t + -0.28 = 0 Multiply -1 * 1.0904936 4.9t2 + -1.0904936t + -0.28 = 0 Reorder the terms: -0.28 + -1.0904936t + 4.9t2 = 0 Solving -0.28 + -1.0904936t + 4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -0.05714285714 + -0.2225497143t + t2 = 0 Move the constant term to the right: Add '0.05714285714' to each side of the equation. -0.05714285714 + -0.2225497143t + 0.05714285714 + t2 = 0 + 0.05714285714 Reorder the terms: -0.05714285714 + 0.05714285714 + -0.2225497143t + t2 = 0 + 0.05714285714 Combine like terms: -0.05714285714 + 0.05714285714 = 0.00000000000 0.00000000000 + -0.2225497143t + t2 = 0 + 0.05714285714 -0.2225497143t + t2 = 0 + 0.05714285714 Combine like terms: 0 + 0.05714285714 = 0.05714285714 -0.2225497143t + t2 = 0.05714285714 The t term is -0.2225497143t. Take half its coefficient (-0.1112748572). Square it (0.01238209384) and add it to both sides. Add '0.01238209384' to each side of the equation. -0.2225497143t + 0.01238209384 + t2 = 0.05714285714 + 0.01238209384 Reorder the terms: 0.01238209384 + -0.2225497143t + t2 = 0.05714285714 + 0.01238209384 Combine like terms: 0.05714285714 + 0.01238209384 = 0.06952495098 0.01238209384 + -0.2225497143t + t2 = 0.06952495098 Factor a perfect square on the left side: (t + -0.1112748572)(t + -0.1112748572) = 0.06952495098 Calculate the square root of the right side: 0.263675845 Break this problem into two subproblems by setting (t + -0.1112748572) equal to 0.263675845 and -0.263675845.Subproblem 1
t + -0.1112748572 = 0.263675845 Simplifying t + -0.1112748572 = 0.263675845 Reorder the terms: -0.1112748572 + t = 0.263675845 Solving -0.1112748572 + t = 0.263675845 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1112748572' to each side of the equation. -0.1112748572 + 0.1112748572 + t = 0.263675845 + 0.1112748572 Combine like terms: -0.1112748572 + 0.1112748572 = 0.0000000000 0.0000000000 + t = 0.263675845 + 0.1112748572 t = 0.263675845 + 0.1112748572 Combine like terms: 0.263675845 + 0.1112748572 = 0.3749507022 t = 0.3749507022 Simplifying t = 0.3749507022Subproblem 2
t + -0.1112748572 = -0.263675845 Simplifying t + -0.1112748572 = -0.263675845 Reorder the terms: -0.1112748572 + t = -0.263675845 Solving -0.1112748572 + t = -0.263675845 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1112748572' to each side of the equation. -0.1112748572 + 0.1112748572 + t = -0.263675845 + 0.1112748572 Combine like terms: -0.1112748572 + 0.1112748572 = 0.0000000000 0.0000000000 + t = -0.263675845 + 0.1112748572 t = -0.263675845 + 0.1112748572 Combine like terms: -0.263675845 + 0.1112748572 = -0.1524009878 t = -0.1524009878 Simplifying t = -0.1524009878Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.3749507022, -0.1524009878}
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