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Simplifying 15 = t(30 + -4.9t) 15 = (30 * t + -4.9t * t) 15 = (30t + -4.9t2) Solving 15 = 30t + -4.9t2 Solving for variable 't'. Reorder the terms: 15 + -30t + 4.9t2 = 30t + -30t + -4.9t2 + 4.9t2 Combine like terms: 30t + -30t = 0 15 + -30t + 4.9t2 = 0 + -4.9t2 + 4.9t2 15 + -30t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 15 + -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'. 3.06122449 + -6.12244898t + t2 = 0 Move the constant term to the right: Add '-3.06122449' to each side of the equation. 3.06122449 + -6.12244898t + -3.06122449 + t2 = 0 + -3.06122449 Reorder the terms: 3.06122449 + -3.06122449 + -6.12244898t + t2 = 0 + -3.06122449 Combine like terms: 3.06122449 + -3.06122449 = 0.00000000 0.00000000 + -6.12244898t + t2 = 0 + -3.06122449 -6.12244898t + t2 = 0 + -3.06122449 Combine like terms: 0 + -3.06122449 = -3.06122449 -6.12244898t + t2 = -3.06122449 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 = -3.06122449 + 9.371095378 Reorder the terms: 9.371095378 + -6.12244898t + t2 = -3.06122449 + 9.371095378 Combine like terms: -3.06122449 + 9.371095378 = 6.309870888 9.371095378 + -6.12244898t + t2 = 6.309870888 Factor a perfect square on the left side: (t + -3.06122449)(t + -3.06122449) = 6.309870888 Calculate the square root of the right side: 2.511945638 Break this problem into two subproblems by setting (t + -3.06122449) equal to 2.511945638 and -2.511945638.Subproblem 1
t + -3.06122449 = 2.511945638 Simplifying t + -3.06122449 = 2.511945638 Reorder the terms: -3.06122449 + t = 2.511945638 Solving -3.06122449 + t = 2.511945638 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 = 2.511945638 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + t = 2.511945638 + 3.06122449 t = 2.511945638 + 3.06122449 Combine like terms: 2.511945638 + 3.06122449 = 5.573170128 t = 5.573170128 Simplifying t = 5.573170128Subproblem 2
t + -3.06122449 = -2.511945638 Simplifying t + -3.06122449 = -2.511945638 Reorder the terms: -3.06122449 + t = -2.511945638 Solving -3.06122449 + t = -2.511945638 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 = -2.511945638 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + t = -2.511945638 + 3.06122449 t = -2.511945638 + 3.06122449 Combine like terms: -2.511945638 + 3.06122449 = 0.549278852 t = 0.549278852 Simplifying t = 0.549278852Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.573170128, 0.549278852}
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