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Simplifying 40 = 4.9t2 + 30t + 12 Reorder the terms: 40 = 12 + 30t + 4.9t2 Solving 40 = 12 + 30t + 4.9t2 Solving for variable 't'. Combine like terms: 40 + -12 = 28 28 + -30t + -4.9t2 = 12 + 30t + 4.9t2 + -12 + -30t + -4.9t2 Reorder the terms: 28 + -30t + -4.9t2 = 12 + -12 + 30t + -30t + 4.9t2 + -4.9t2 Combine like terms: 12 + -12 = 0 28 + -30t + -4.9t2 = 0 + 30t + -30t + 4.9t2 + -4.9t2 28 + -30t + -4.9t2 = 30t + -30t + 4.9t2 + -4.9t2 Combine like terms: 30t + -30t = 0 28 + -30t + -4.9t2 = 0 + 4.9t2 + -4.9t2 28 + -30t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 28 + -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'. -5.714285714 + 6.12244898t + t2 = 0 Move the constant term to the right: Add '5.714285714' to each side of the equation. -5.714285714 + 6.12244898t + 5.714285714 + t2 = 0 + 5.714285714 Reorder the terms: -5.714285714 + 5.714285714 + 6.12244898t + t2 = 0 + 5.714285714 Combine like terms: -5.714285714 + 5.714285714 = 0.000000000 0.000000000 + 6.12244898t + t2 = 0 + 5.714285714 6.12244898t + t2 = 0 + 5.714285714 Combine like terms: 0 + 5.714285714 = 5.714285714 6.12244898t + t2 = 5.714285714 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 = 5.714285714 + 9.371095378 Reorder the terms: 9.371095378 + 6.12244898t + t2 = 5.714285714 + 9.371095378 Combine like terms: 5.714285714 + 9.371095378 = 15.085381092 9.371095378 + 6.12244898t + t2 = 15.085381092 Factor a perfect square on the left side: (t + 3.06122449)(t + 3.06122449) = 15.085381092 Calculate the square root of the right side: 3.883990357 Break this problem into two subproblems by setting (t + 3.06122449) equal to 3.883990357 and -3.883990357.Subproblem 1
t + 3.06122449 = 3.883990357 Simplifying t + 3.06122449 = 3.883990357 Reorder the terms: 3.06122449 + t = 3.883990357 Solving 3.06122449 + t = 3.883990357 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 = 3.883990357 + -3.06122449 Combine like terms: 3.06122449 + -3.06122449 = 0.00000000 0.00000000 + t = 3.883990357 + -3.06122449 t = 3.883990357 + -3.06122449 Combine like terms: 3.883990357 + -3.06122449 = 0.822765867 t = 0.822765867 Simplifying t = 0.822765867Subproblem 2
t + 3.06122449 = -3.883990357 Simplifying t + 3.06122449 = -3.883990357 Reorder the terms: 3.06122449 + t = -3.883990357 Solving 3.06122449 + t = -3.883990357 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 = -3.883990357 + -3.06122449 Combine like terms: 3.06122449 + -3.06122449 = 0.00000000 0.00000000 + t = -3.883990357 + -3.06122449 t = -3.883990357 + -3.06122449 Combine like terms: -3.883990357 + -3.06122449 = -6.945214847 t = -6.945214847 Simplifying t = -6.945214847Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.822765867, -6.945214847}
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