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Simplifying 77 = -14t + 4.9t2 Solving 77 = -14t + 4.9t2 Solving for variable 't'. Reorder the terms: 77 + 14t + -4.9t2 = -14t + 14t + 4.9t2 + -4.9t2 Combine like terms: -14t + 14t = 0 77 + 14t + -4.9t2 = 0 + 4.9t2 + -4.9t2 77 + 14t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 77 + 14t + -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'. -15.71428571 + -2.857142857t + t2 = 0 Move the constant term to the right: Add '15.71428571' to each side of the equation. -15.71428571 + -2.857142857t + 15.71428571 + t2 = 0 + 15.71428571 Reorder the terms: -15.71428571 + 15.71428571 + -2.857142857t + t2 = 0 + 15.71428571 Combine like terms: -15.71428571 + 15.71428571 = 0.00000000 0.00000000 + -2.857142857t + t2 = 0 + 15.71428571 -2.857142857t + t2 = 0 + 15.71428571 Combine like terms: 0 + 15.71428571 = 15.71428571 -2.857142857t + t2 = 15.71428571 The t term is -2.857142857t. Take half its coefficient (-1.428571429). Square it (2.040816328) and add it to both sides. Add '2.040816328' to each side of the equation. -2.857142857t + 2.040816328 + t2 = 15.71428571 + 2.040816328 Reorder the terms: 2.040816328 + -2.857142857t + t2 = 15.71428571 + 2.040816328 Combine like terms: 15.71428571 + 2.040816328 = 17.755102038 2.040816328 + -2.857142857t + t2 = 17.755102038 Factor a perfect square on the left side: (t + -1.428571429)(t + -1.428571429) = 17.755102038 Calculate the square root of the right side: 4.213680344 Break this problem into two subproblems by setting (t + -1.428571429) equal to 4.213680344 and -4.213680344.Subproblem 1
t + -1.428571429 = 4.213680344 Simplifying t + -1.428571429 = 4.213680344 Reorder the terms: -1.428571429 + t = 4.213680344 Solving -1.428571429 + t = 4.213680344 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + t = 4.213680344 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + t = 4.213680344 + 1.428571429 t = 4.213680344 + 1.428571429 Combine like terms: 4.213680344 + 1.428571429 = 5.642251773 t = 5.642251773 Simplifying t = 5.642251773Subproblem 2
t + -1.428571429 = -4.213680344 Simplifying t + -1.428571429 = -4.213680344 Reorder the terms: -1.428571429 + t = -4.213680344 Solving -1.428571429 + t = -4.213680344 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + t = -4.213680344 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + t = -4.213680344 + 1.428571429 t = -4.213680344 + 1.428571429 Combine like terms: -4.213680344 + 1.428571429 = -2.785108915 t = -2.785108915 Simplifying t = -2.785108915Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.642251773, -2.785108915}
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