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Simplifying 0 = 4.9t2 + -11t + -92 Reorder the terms: 0 = -92 + -11t + 4.9t2 Solving 0 = -92 + -11t + 4.9t2 Solving for variable 't'. Combine like terms: 0 + 92 = 92 92 + 11t + -4.9t2 = -92 + -11t + 4.9t2 + 92 + 11t + -4.9t2 Reorder the terms: 92 + 11t + -4.9t2 = -92 + 92 + -11t + 11t + 4.9t2 + -4.9t2 Combine like terms: -92 + 92 = 0 92 + 11t + -4.9t2 = 0 + -11t + 11t + 4.9t2 + -4.9t2 92 + 11t + -4.9t2 = -11t + 11t + 4.9t2 + -4.9t2 Combine like terms: -11t + 11t = 0 92 + 11t + -4.9t2 = 0 + 4.9t2 + -4.9t2 92 + 11t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 92 + 11t + -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'. -18.7755102 + -2.244897959t + t2 = 0 Move the constant term to the right: Add '18.7755102' to each side of the equation. -18.7755102 + -2.244897959t + 18.7755102 + t2 = 0 + 18.7755102 Reorder the terms: -18.7755102 + 18.7755102 + -2.244897959t + t2 = 0 + 18.7755102 Combine like terms: -18.7755102 + 18.7755102 = 0.0000000 0.0000000 + -2.244897959t + t2 = 0 + 18.7755102 -2.244897959t + t2 = 0 + 18.7755102 Combine like terms: 0 + 18.7755102 = 18.7755102 -2.244897959t + t2 = 18.7755102 The t term is -2.244897959t. Take half its coefficient (-1.12244898). Square it (1.259891713) and add it to both sides. Add '1.259891713' to each side of the equation. -2.244897959t + 1.259891713 + t2 = 18.7755102 + 1.259891713 Reorder the terms: 1.259891713 + -2.244897959t + t2 = 18.7755102 + 1.259891713 Combine like terms: 18.7755102 + 1.259891713 = 20.035401913 1.259891713 + -2.244897959t + t2 = 20.035401913 Factor a perfect square on the left side: (t + -1.12244898)(t + -1.12244898) = 20.035401913 Calculate the square root of the right side: 4.476092259 Break this problem into two subproblems by setting (t + -1.12244898) equal to 4.476092259 and -4.476092259.Subproblem 1
t + -1.12244898 = 4.476092259 Simplifying t + -1.12244898 = 4.476092259 Reorder the terms: -1.12244898 + t = 4.476092259 Solving -1.12244898 + t = 4.476092259 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.12244898' to each side of the equation. -1.12244898 + 1.12244898 + t = 4.476092259 + 1.12244898 Combine like terms: -1.12244898 + 1.12244898 = 0.00000000 0.00000000 + t = 4.476092259 + 1.12244898 t = 4.476092259 + 1.12244898 Combine like terms: 4.476092259 + 1.12244898 = 5.598541239 t = 5.598541239 Simplifying t = 5.598541239Subproblem 2
t + -1.12244898 = -4.476092259 Simplifying t + -1.12244898 = -4.476092259 Reorder the terms: -1.12244898 + t = -4.476092259 Solving -1.12244898 + t = -4.476092259 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.12244898' to each side of the equation. -1.12244898 + 1.12244898 + t = -4.476092259 + 1.12244898 Combine like terms: -1.12244898 + 1.12244898 = 0.00000000 0.00000000 + t = -4.476092259 + 1.12244898 t = -4.476092259 + 1.12244898 Combine like terms: -4.476092259 + 1.12244898 = -3.353643279 t = -3.353643279 Simplifying t = -3.353643279Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.598541239, -3.353643279}
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