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Simplifying 0 = 1 + 25t + -9.8t2 Solving 0 = 1 + 25t + -9.8t2 Solving for variable 't'. Combine like terms: 0 + -1 = -1 -1 + -25t + 9.8t2 = 1 + 25t + -9.8t2 + -1 + -25t + 9.8t2 Reorder the terms: -1 + -25t + 9.8t2 = 1 + -1 + 25t + -25t + -9.8t2 + 9.8t2 Combine like terms: 1 + -1 = 0 -1 + -25t + 9.8t2 = 0 + 25t + -25t + -9.8t2 + 9.8t2 -1 + -25t + 9.8t2 = 25t + -25t + -9.8t2 + 9.8t2 Combine like terms: 25t + -25t = 0 -1 + -25t + 9.8t2 = 0 + -9.8t2 + 9.8t2 -1 + -25t + 9.8t2 = -9.8t2 + 9.8t2 Combine like terms: -9.8t2 + 9.8t2 = 0.0 -1 + -25t + 9.8t2 = 0.0 Begin completing the square. Divide all terms by 9.8 the coefficient of the squared term: Divide each side by '9.8'. -0.1020408163 + -2.551020408t + t2 = 0 Move the constant term to the right: Add '0.1020408163' to each side of the equation. -0.1020408163 + -2.551020408t + 0.1020408163 + t2 = 0 + 0.1020408163 Reorder the terms: -0.1020408163 + 0.1020408163 + -2.551020408t + t2 = 0 + 0.1020408163 Combine like terms: -0.1020408163 + 0.1020408163 = 0.0000000000 0.0000000000 + -2.551020408t + t2 = 0 + 0.1020408163 -2.551020408t + t2 = 0 + 0.1020408163 Combine like terms: 0 + 0.1020408163 = 0.1020408163 -2.551020408t + t2 = 0.1020408163 The t term is -2.551020408t. Take half its coefficient (-1.275510204). Square it (1.626926281) and add it to both sides. Add '1.626926281' to each side of the equation. -2.551020408t + 1.626926281 + t2 = 0.1020408163 + 1.626926281 Reorder the terms: 1.626926281 + -2.551020408t + t2 = 0.1020408163 + 1.626926281 Combine like terms: 0.1020408163 + 1.626926281 = 1.7289670973 1.626926281 + -2.551020408t + t2 = 1.7289670973 Factor a perfect square on the left side: (t + -1.275510204)(t + -1.275510204) = 1.7289670973 Calculate the square root of the right side: 1.314901934 Break this problem into two subproblems by setting (t + -1.275510204) equal to 1.314901934 and -1.314901934.Subproblem 1
t + -1.275510204 = 1.314901934 Simplifying t + -1.275510204 = 1.314901934 Reorder the terms: -1.275510204 + t = 1.314901934 Solving -1.275510204 + t = 1.314901934 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.275510204' to each side of the equation. -1.275510204 + 1.275510204 + t = 1.314901934 + 1.275510204 Combine like terms: -1.275510204 + 1.275510204 = 0.000000000 0.000000000 + t = 1.314901934 + 1.275510204 t = 1.314901934 + 1.275510204 Combine like terms: 1.314901934 + 1.275510204 = 2.590412138 t = 2.590412138 Simplifying t = 2.590412138Subproblem 2
t + -1.275510204 = -1.314901934 Simplifying t + -1.275510204 = -1.314901934 Reorder the terms: -1.275510204 + t = -1.314901934 Solving -1.275510204 + t = -1.314901934 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.275510204' to each side of the equation. -1.275510204 + 1.275510204 + t = -1.314901934 + 1.275510204 Combine like terms: -1.275510204 + 1.275510204 = 0.000000000 0.000000000 + t = -1.314901934 + 1.275510204 t = -1.314901934 + 1.275510204 Combine like terms: -1.314901934 + 1.275510204 = -0.03939173 t = -0.03939173 Simplifying t = -0.03939173Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.590412138, -0.03939173}
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