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Simplifying 8 = 15t + -4.9t2 Solving 8 = 15t + -4.9t2 Solving for variable 't'. Reorder the terms: 8 + -15t + 4.9t2 = 15t + -15t + -4.9t2 + 4.9t2 Combine like terms: 15t + -15t = 0 8 + -15t + 4.9t2 = 0 + -4.9t2 + 4.9t2 8 + -15t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 8 + -15t + 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'. 1.632653061 + -3.06122449t + t2 = 0 Move the constant term to the right: Add '-1.632653061' to each side of the equation. 1.632653061 + -3.06122449t + -1.632653061 + t2 = 0 + -1.632653061 Reorder the terms: 1.632653061 + -1.632653061 + -3.06122449t + t2 = 0 + -1.632653061 Combine like terms: 1.632653061 + -1.632653061 = 0.000000000 0.000000000 + -3.06122449t + t2 = 0 + -1.632653061 -3.06122449t + t2 = 0 + -1.632653061 Combine like terms: 0 + -1.632653061 = -1.632653061 -3.06122449t + t2 = -1.632653061 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 = -1.632653061 + 2.342773845 Reorder the terms: 2.342773845 + -3.06122449t + t2 = -1.632653061 + 2.342773845 Combine like terms: -1.632653061 + 2.342773845 = 0.710120784 2.342773845 + -3.06122449t + t2 = 0.710120784 Factor a perfect square on the left side: (t + -1.530612245)(t + -1.530612245) = 0.710120784 Calculate the square root of the right side: 0.842686646 Break this problem into two subproblems by setting (t + -1.530612245) equal to 0.842686646 and -0.842686646.Subproblem 1
t + -1.530612245 = 0.842686646 Simplifying t + -1.530612245 = 0.842686646 Reorder the terms: -1.530612245 + t = 0.842686646 Solving -1.530612245 + t = 0.842686646 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 = 0.842686646 + 1.530612245 Combine like terms: -1.530612245 + 1.530612245 = 0.000000000 0.000000000 + t = 0.842686646 + 1.530612245 t = 0.842686646 + 1.530612245 Combine like terms: 0.842686646 + 1.530612245 = 2.373298891 t = 2.373298891 Simplifying t = 2.373298891Subproblem 2
t + -1.530612245 = -0.842686646 Simplifying t + -1.530612245 = -0.842686646 Reorder the terms: -1.530612245 + t = -0.842686646 Solving -1.530612245 + t = -0.842686646 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 = -0.842686646 + 1.530612245 Combine like terms: -1.530612245 + 1.530612245 = 0.000000000 0.000000000 + t = -0.842686646 + 1.530612245 t = -0.842686646 + 1.530612245 Combine like terms: -0.842686646 + 1.530612245 = 0.687925599 t = 0.687925599 Simplifying t = 0.687925599Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.373298891, 0.687925599}
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