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Simplifying 0 = -4.9t2 + 32t + 2 Reorder the terms: 0 = 2 + 32t + -4.9t2 Solving 0 = 2 + 32t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -2 = -2 -2 + -32t + 4.9t2 = 2 + 32t + -4.9t2 + -2 + -32t + 4.9t2 Reorder the terms: -2 + -32t + 4.9t2 = 2 + -2 + 32t + -32t + -4.9t2 + 4.9t2 Combine like terms: 2 + -2 = 0 -2 + -32t + 4.9t2 = 0 + 32t + -32t + -4.9t2 + 4.9t2 -2 + -32t + 4.9t2 = 32t + -32t + -4.9t2 + 4.9t2 Combine like terms: 32t + -32t = 0 -2 + -32t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -2 + -32t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -2 + -32t + 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 + -6.530612245t + t2 = 0 Move the constant term to the right: Add '0.4081632653' to each side of the equation. -0.4081632653 + -6.530612245t + 0.4081632653 + t2 = 0 + 0.4081632653 Reorder the terms: -0.4081632653 + 0.4081632653 + -6.530612245t + t2 = 0 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + -6.530612245t + t2 = 0 + 0.4081632653 -6.530612245t + t2 = 0 + 0.4081632653 Combine like terms: 0 + 0.4081632653 = 0.4081632653 -6.530612245t + t2 = 0.4081632653 The t term is -6.530612245t. Take half its coefficient (-3.265306123). Square it (10.66222408) and add it to both sides. Add '10.66222408' to each side of the equation. -6.530612245t + 10.66222408 + t2 = 0.4081632653 + 10.66222408 Reorder the terms: 10.66222408 + -6.530612245t + t2 = 0.4081632653 + 10.66222408 Combine like terms: 0.4081632653 + 10.66222408 = 11.0703873453 10.66222408 + -6.530612245t + t2 = 11.0703873453 Factor a perfect square on the left side: (t + -3.265306123)(t + -3.265306123) = 11.0703873453 Calculate the square root of the right side: 3.327219161 Break this problem into two subproblems by setting (t + -3.265306123) equal to 3.327219161 and -3.327219161.Subproblem 1
t + -3.265306123 = 3.327219161 Simplifying t + -3.265306123 = 3.327219161 Reorder the terms: -3.265306123 + t = 3.327219161 Solving -3.265306123 + t = 3.327219161 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.265306123' to each side of the equation. -3.265306123 + 3.265306123 + t = 3.327219161 + 3.265306123 Combine like terms: -3.265306123 + 3.265306123 = 0.000000000 0.000000000 + t = 3.327219161 + 3.265306123 t = 3.327219161 + 3.265306123 Combine like terms: 3.327219161 + 3.265306123 = 6.592525284 t = 6.592525284 Simplifying t = 6.592525284Subproblem 2
t + -3.265306123 = -3.327219161 Simplifying t + -3.265306123 = -3.327219161 Reorder the terms: -3.265306123 + t = -3.327219161 Solving -3.265306123 + t = -3.327219161 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.265306123' to each side of the equation. -3.265306123 + 3.265306123 + t = -3.327219161 + 3.265306123 Combine like terms: -3.265306123 + 3.265306123 = 0.000000000 0.000000000 + t = -3.327219161 + 3.265306123 t = -3.327219161 + 3.265306123 Combine like terms: -3.327219161 + 3.265306123 = -0.061913038 t = -0.061913038 Simplifying t = -0.061913038Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.592525284, -0.061913038}
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