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Simplifying -16.1t2 + 50t + -4 = 0 Reorder the terms: -4 + 50t + -16.1t2 = 0 Solving -4 + 50t + -16.1t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -16.1 the coefficient of the squared term: Divide each side by '-16.1'. 0.248447205 + -3.105590062t + t2 = 0 Move the constant term to the right: Add '-0.248447205' to each side of the equation. 0.248447205 + -3.105590062t + -0.248447205 + t2 = 0 + -0.248447205 Reorder the terms: 0.248447205 + -0.248447205 + -3.105590062t + t2 = 0 + -0.248447205 Combine like terms: 0.248447205 + -0.248447205 = 0.000000000 0.000000000 + -3.105590062t + t2 = 0 + -0.248447205 -3.105590062t + t2 = 0 + -0.248447205 Combine like terms: 0 + -0.248447205 = -0.248447205 -3.105590062t + t2 = -0.248447205 The t term is -3.105590062t. Take half its coefficient (-1.552795031). Square it (2.411172408) and add it to both sides. Add '2.411172408' to each side of the equation. -3.105590062t + 2.411172408 + t2 = -0.248447205 + 2.411172408 Reorder the terms: 2.411172408 + -3.105590062t + t2 = -0.248447205 + 2.411172408 Combine like terms: -0.248447205 + 2.411172408 = 2.162725203 2.411172408 + -3.105590062t + t2 = 2.162725203 Factor a perfect square on the left side: (t + -1.552795031)(t + -1.552795031) = 2.162725203 Calculate the square root of the right side: 1.470620686 Break this problem into two subproblems by setting (t + -1.552795031) equal to 1.470620686 and -1.470620686.Subproblem 1
t + -1.552795031 = 1.470620686 Simplifying t + -1.552795031 = 1.470620686 Reorder the terms: -1.552795031 + t = 1.470620686 Solving -1.552795031 + t = 1.470620686 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.552795031' to each side of the equation. -1.552795031 + 1.552795031 + t = 1.470620686 + 1.552795031 Combine like terms: -1.552795031 + 1.552795031 = 0.000000000 0.000000000 + t = 1.470620686 + 1.552795031 t = 1.470620686 + 1.552795031 Combine like terms: 1.470620686 + 1.552795031 = 3.023415717 t = 3.023415717 Simplifying t = 3.023415717Subproblem 2
t + -1.552795031 = -1.470620686 Simplifying t + -1.552795031 = -1.470620686 Reorder the terms: -1.552795031 + t = -1.470620686 Solving -1.552795031 + t = -1.470620686 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.552795031' to each side of the equation. -1.552795031 + 1.552795031 + t = -1.470620686 + 1.552795031 Combine like terms: -1.552795031 + 1.552795031 = 0.000000000 0.000000000 + t = -1.470620686 + 1.552795031 t = -1.470620686 + 1.552795031 Combine like terms: -1.470620686 + 1.552795031 = 0.082174345 t = 0.082174345 Simplifying t = 0.082174345Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.023415717, 0.082174345}
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