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Simplifying 0 = 2 + 23.5t + -4.9t2 Solving 0 = 2 + 23.5t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -2 = -2 -2 + -23.5t + 4.9t2 = 2 + 23.5t + -4.9t2 + -2 + -23.5t + 4.9t2 Reorder the terms: -2 + -23.5t + 4.9t2 = 2 + -2 + 23.5t + -23.5t + -4.9t2 + 4.9t2 Combine like terms: 2 + -2 = 0 -2 + -23.5t + 4.9t2 = 0 + 23.5t + -23.5t + -4.9t2 + 4.9t2 -2 + -23.5t + 4.9t2 = 23.5t + -23.5t + -4.9t2 + 4.9t2 Combine like terms: 23.5t + -23.5t = 0.0 -2 + -23.5t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 -2 + -23.5t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -2 + -23.5t + 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'. -0.4081632653 + -4.795918367t + t2 = 0 Move the constant term to the right: Add '0.4081632653' to each side of the equation. -0.4081632653 + -4.795918367t + 0.4081632653 + t2 = 0 + 0.4081632653 Reorder the terms: -0.4081632653 + 0.4081632653 + -4.795918367t + t2 = 0 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + -4.795918367t + t2 = 0 + 0.4081632653 -4.795918367t + t2 = 0 + 0.4081632653 Combine like terms: 0 + 0.4081632653 = 0.4081632653 -4.795918367t + t2 = 0.4081632653 The t term is -4.795918367t. Take half its coefficient (-2.397959184). Square it (5.750208248) and add it to both sides. Add '5.750208248' to each side of the equation. -4.795918367t + 5.750208248 + t2 = 0.4081632653 + 5.750208248 Reorder the terms: 5.750208248 + -4.795918367t + t2 = 0.4081632653 + 5.750208248 Combine like terms: 0.4081632653 + 5.750208248 = 6.1583715133 5.750208248 + -4.795918367t + t2 = 6.1583715133 Factor a perfect square on the left side: (t + -2.397959184)(t + -2.397959184) = 6.1583715133 Calculate the square root of the right side: 2.48160664 Break this problem into two subproblems by setting (t + -2.397959184) equal to 2.48160664 and -2.48160664.Subproblem 1
t + -2.397959184 = 2.48160664 Simplifying t + -2.397959184 = 2.48160664 Reorder the terms: -2.397959184 + t = 2.48160664 Solving -2.397959184 + t = 2.48160664 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.397959184' to each side of the equation. -2.397959184 + 2.397959184 + t = 2.48160664 + 2.397959184 Combine like terms: -2.397959184 + 2.397959184 = 0.000000000 0.000000000 + t = 2.48160664 + 2.397959184 t = 2.48160664 + 2.397959184 Combine like terms: 2.48160664 + 2.397959184 = 4.879565824 t = 4.879565824 Simplifying t = 4.879565824Subproblem 2
t + -2.397959184 = -2.48160664 Simplifying t + -2.397959184 = -2.48160664 Reorder the terms: -2.397959184 + t = -2.48160664 Solving -2.397959184 + t = -2.48160664 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.397959184' to each side of the equation. -2.397959184 + 2.397959184 + t = -2.48160664 + 2.397959184 Combine like terms: -2.397959184 + 2.397959184 = 0.000000000 0.000000000 + t = -2.48160664 + 2.397959184 t = -2.48160664 + 2.397959184 Combine like terms: -2.48160664 + 2.397959184 = -0.083647456 t = -0.083647456 Simplifying t = -0.083647456Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.879565824, -0.083647456}
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