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Simplifying 0.5 + 15(t) + 4.9(t2) = 0 Solving 0.5 + 15t + 4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. 0.1020408163 + 3.06122449t + t2 = 0 Move the constant term to the right: Add '-0.1020408163' to each side of the equation. 0.1020408163 + 3.06122449t + -0.1020408163 + t2 = 0 + -0.1020408163 Reorder the terms: 0.1020408163 + -0.1020408163 + 3.06122449t + t2 = 0 + -0.1020408163 Combine like terms: 0.1020408163 + -0.1020408163 = 0.0000000000 0.0000000000 + 3.06122449t + t2 = 0 + -0.1020408163 3.06122449t + t2 = 0 + -0.1020408163 Combine like terms: 0 + -0.1020408163 = -0.1020408163 3.06122449t + t2 = -0.1020408163 The t term is 3.06122449t. Take half its coefficient (1.530612245). Square it (2.342773845) and add it to both sides. Add '2.342773845' to each side of the equation. 3.06122449t + 2.342773845 + t2 = -0.1020408163 + 2.342773845 Reorder the terms: 2.342773845 + 3.06122449t + t2 = -0.1020408163 + 2.342773845 Combine like terms: -0.1020408163 + 2.342773845 = 2.2407330287 2.342773845 + 3.06122449t + t2 = 2.2407330287 Factor a perfect square on the left side: (t + 1.530612245)(t + 1.530612245) = 2.2407330287 Calculate the square root of the right side: 1.496907822 Break this problem into two subproblems by setting (t + 1.530612245) equal to 1.496907822 and -1.496907822.Subproblem 1
t + 1.530612245 = 1.496907822 Simplifying t + 1.530612245 = 1.496907822 Reorder the terms: 1.530612245 + t = 1.496907822 Solving 1.530612245 + t = 1.496907822 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.530612245' to each side of the equation. 1.530612245 + -1.530612245 + t = 1.496907822 + -1.530612245 Combine like terms: 1.530612245 + -1.530612245 = 0.000000000 0.000000000 + t = 1.496907822 + -1.530612245 t = 1.496907822 + -1.530612245 Combine like terms: 1.496907822 + -1.530612245 = -0.033704423 t = -0.033704423 Simplifying t = -0.033704423Subproblem 2
t + 1.530612245 = -1.496907822 Simplifying t + 1.530612245 = -1.496907822 Reorder the terms: 1.530612245 + t = -1.496907822 Solving 1.530612245 + t = -1.496907822 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.530612245' to each side of the equation. 1.530612245 + -1.530612245 + t = -1.496907822 + -1.530612245 Combine like terms: 1.530612245 + -1.530612245 = 0.000000000 0.000000000 + t = -1.496907822 + -1.530612245 t = -1.496907822 + -1.530612245 Combine like terms: -1.496907822 + -1.530612245 = -3.027520067 t = -3.027520067 Simplifying t = -3.027520067Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.033704423, -3.027520067}
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