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Simplifying t = -4.9t2 + 19.6t + 1 Reorder the terms: t = 1 + 19.6t + -4.9t2 Solving t = 1 + 19.6t + -4.9t2 Solving for variable 't'. Reorder the terms: -1 + t + -19.6t + 4.9t2 = 1 + 19.6t + -4.9t2 + -1 + -19.6t + 4.9t2 Combine like terms: t + -19.6t = -18.6t -1 + -18.6t + 4.9t2 = 1 + 19.6t + -4.9t2 + -1 + -19.6t + 4.9t2 Reorder the terms: -1 + -18.6t + 4.9t2 = 1 + -1 + 19.6t + -19.6t + -4.9t2 + 4.9t2 Combine like terms: 1 + -1 = 0 -1 + -18.6t + 4.9t2 = 0 + 19.6t + -19.6t + -4.9t2 + 4.9t2 -1 + -18.6t + 4.9t2 = 19.6t + -19.6t + -4.9t2 + 4.9t2 Combine like terms: 19.6t + -19.6t = 0.0 -1 + -18.6t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 -1 + -18.6t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -1 + -18.6t + 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'. -0.2040816327 + -3.795918367t + t2 = 0 Move the constant term to the right: Add '0.2040816327' to each side of the equation. -0.2040816327 + -3.795918367t + 0.2040816327 + t2 = 0 + 0.2040816327 Reorder the terms: -0.2040816327 + 0.2040816327 + -3.795918367t + t2 = 0 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + -3.795918367t + t2 = 0 + 0.2040816327 -3.795918367t + t2 = 0 + 0.2040816327 Combine like terms: 0 + 0.2040816327 = 0.2040816327 -3.795918367t + t2 = 0.2040816327 The t term is -3.795918367t. Take half its coefficient (-1.897959184). Square it (3.602249064) and add it to both sides. Add '3.602249064' to each side of the equation. -3.795918367t + 3.602249064 + t2 = 0.2040816327 + 3.602249064 Reorder the terms: 3.602249064 + -3.795918367t + t2 = 0.2040816327 + 3.602249064 Combine like terms: 0.2040816327 + 3.602249064 = 3.8063306967 3.602249064 + -3.795918367t + t2 = 3.8063306967 Factor a perfect square on the left side: (t + -1.897959184)(t + -1.897959184) = 3.8063306967 Calculate the square root of the right side: 1.950981983 Break this problem into two subproblems by setting (t + -1.897959184) equal to 1.950981983 and -1.950981983.Subproblem 1
t + -1.897959184 = 1.950981983 Simplifying t + -1.897959184 = 1.950981983 Reorder the terms: -1.897959184 + t = 1.950981983 Solving -1.897959184 + t = 1.950981983 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.897959184' to each side of the equation. -1.897959184 + 1.897959184 + t = 1.950981983 + 1.897959184 Combine like terms: -1.897959184 + 1.897959184 = 0.000000000 0.000000000 + t = 1.950981983 + 1.897959184 t = 1.950981983 + 1.897959184 Combine like terms: 1.950981983 + 1.897959184 = 3.848941167 t = 3.848941167 Simplifying t = 3.848941167Subproblem 2
t + -1.897959184 = -1.950981983 Simplifying t + -1.897959184 = -1.950981983 Reorder the terms: -1.897959184 + t = -1.950981983 Solving -1.897959184 + t = -1.950981983 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.897959184' to each side of the equation. -1.897959184 + 1.897959184 + t = -1.950981983 + 1.897959184 Combine like terms: -1.897959184 + 1.897959184 = 0.000000000 0.000000000 + t = -1.950981983 + 1.897959184 t = -1.950981983 + 1.897959184 Combine like terms: -1.950981983 + 1.897959184 = -0.053022799 t = -0.053022799 Simplifying t = -0.053022799Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.848941167, -0.053022799}
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