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Simplifying -4.9t2 + 40t = 24 Reorder the terms: 40t + -4.9t2 = 24 Solving 40t + -4.9t2 = 24 Solving for variable 't'. Reorder the terms: -24 + 40t + -4.9t2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + 40t + -4.9t2 = 0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. 4.897959184 + -8.163265306t + t2 = 0 Move the constant term to the right: Add '-4.897959184' to each side of the equation. 4.897959184 + -8.163265306t + -4.897959184 + t2 = 0 + -4.897959184 Reorder the terms: 4.897959184 + -4.897959184 + -8.163265306t + t2 = 0 + -4.897959184 Combine like terms: 4.897959184 + -4.897959184 = 0.000000000 0.000000000 + -8.163265306t + t2 = 0 + -4.897959184 -8.163265306t + t2 = 0 + -4.897959184 Combine like terms: 0 + -4.897959184 = -4.897959184 -8.163265306t + t2 = -4.897959184 The t term is -8.163265306t. Take half its coefficient (-4.081632653). Square it (16.65972511) and add it to both sides. Add '16.65972511' to each side of the equation. -8.163265306t + 16.65972511 + t2 = -4.897959184 + 16.65972511 Reorder the terms: 16.65972511 + -8.163265306t + t2 = -4.897959184 + 16.65972511 Combine like terms: -4.897959184 + 16.65972511 = 11.761765926 16.65972511 + -8.163265306t + t2 = 11.761765926 Factor a perfect square on the left side: (t + -4.081632653)(t + -4.081632653) = 11.761765926 Calculate the square root of the right side: 3.429543107 Break this problem into two subproblems by setting (t + -4.081632653) equal to 3.429543107 and -3.429543107.Subproblem 1
t + -4.081632653 = 3.429543107 Simplifying t + -4.081632653 = 3.429543107 Reorder the terms: -4.081632653 + t = 3.429543107 Solving -4.081632653 + t = 3.429543107 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.081632653' to each side of the equation. -4.081632653 + 4.081632653 + t = 3.429543107 + 4.081632653 Combine like terms: -4.081632653 + 4.081632653 = 0.000000000 0.000000000 + t = 3.429543107 + 4.081632653 t = 3.429543107 + 4.081632653 Combine like terms: 3.429543107 + 4.081632653 = 7.51117576 t = 7.51117576 Simplifying t = 7.51117576Subproblem 2
t + -4.081632653 = -3.429543107 Simplifying t + -4.081632653 = -3.429543107 Reorder the terms: -4.081632653 + t = -3.429543107 Solving -4.081632653 + t = -3.429543107 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.081632653' to each side of the equation. -4.081632653 + 4.081632653 + t = -3.429543107 + 4.081632653 Combine like terms: -4.081632653 + 4.081632653 = 0.000000000 0.000000000 + t = -3.429543107 + 4.081632653 t = -3.429543107 + 4.081632653 Combine like terms: -3.429543107 + 4.081632653 = 0.652089546 t = 0.652089546 Simplifying t = 0.652089546Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.51117576, 0.652089546}
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