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Simplifying 75 = 4.9t2 + 30t Reorder the terms: 75 = 30t + 4.9t2 Solving 75 = 30t + 4.9t2 Solving for variable 't'. Reorder the terms: 75 + -30t + -4.9t2 = 30t + -30t + 4.9t2 + -4.9t2 Combine like terms: 30t + -30t = 0 75 + -30t + -4.9t2 = 0 + 4.9t2 + -4.9t2 75 + -30t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 75 + -30t + -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'. -15.30612245 + 6.12244898t + t2 = 0 Move the constant term to the right: Add '15.30612245' to each side of the equation. -15.30612245 + 6.12244898t + 15.30612245 + t2 = 0 + 15.30612245 Reorder the terms: -15.30612245 + 15.30612245 + 6.12244898t + t2 = 0 + 15.30612245 Combine like terms: -15.30612245 + 15.30612245 = 0.00000000 0.00000000 + 6.12244898t + t2 = 0 + 15.30612245 6.12244898t + t2 = 0 + 15.30612245 Combine like terms: 0 + 15.30612245 = 15.30612245 6.12244898t + t2 = 15.30612245 The t term is 6.12244898t. Take half its coefficient (3.06122449). Square it (9.371095378) and add it to both sides. Add '9.371095378' to each side of the equation. 6.12244898t + 9.371095378 + t2 = 15.30612245 + 9.371095378 Reorder the terms: 9.371095378 + 6.12244898t + t2 = 15.30612245 + 9.371095378 Combine like terms: 15.30612245 + 9.371095378 = 24.677217828 9.371095378 + 6.12244898t + t2 = 24.677217828 Factor a perfect square on the left side: (t + 3.06122449)(t + 3.06122449) = 24.677217828 Calculate the square root of the right side: 4.967616916 Break this problem into two subproblems by setting (t + 3.06122449) equal to 4.967616916 and -4.967616916.Subproblem 1
t + 3.06122449 = 4.967616916 Simplifying t + 3.06122449 = 4.967616916 Reorder the terms: 3.06122449 + t = 4.967616916 Solving 3.06122449 + t = 4.967616916 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.06122449' to each side of the equation. 3.06122449 + -3.06122449 + t = 4.967616916 + -3.06122449 Combine like terms: 3.06122449 + -3.06122449 = 0.00000000 0.00000000 + t = 4.967616916 + -3.06122449 t = 4.967616916 + -3.06122449 Combine like terms: 4.967616916 + -3.06122449 = 1.906392426 t = 1.906392426 Simplifying t = 1.906392426Subproblem 2
t + 3.06122449 = -4.967616916 Simplifying t + 3.06122449 = -4.967616916 Reorder the terms: 3.06122449 + t = -4.967616916 Solving 3.06122449 + t = -4.967616916 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.06122449' to each side of the equation. 3.06122449 + -3.06122449 + t = -4.967616916 + -3.06122449 Combine like terms: 3.06122449 + -3.06122449 = 0.00000000 0.00000000 + t = -4.967616916 + -3.06122449 t = -4.967616916 + -3.06122449 Combine like terms: -4.967616916 + -3.06122449 = -8.028841406 t = -8.028841406 Simplifying t = -8.028841406Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.906392426, -8.028841406}
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