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Simplifying 0 = 4.9t2 + 24.5t + 8.9 Reorder the terms: 0 = 8.9 + 24.5t + 4.9t2 Solving 0 = 8.9 + 24.5t + 4.9t2 Solving for variable 't'. Combine like terms: 0 + -8.9 = -8.9 -8.9 + -24.5t + -4.9t2 = 8.9 + 24.5t + 4.9t2 + -8.9 + -24.5t + -4.9t2 Reorder the terms: -8.9 + -24.5t + -4.9t2 = 8.9 + -8.9 + 24.5t + -24.5t + 4.9t2 + -4.9t2 Combine like terms: 8.9 + -8.9 = 0.0 -8.9 + -24.5t + -4.9t2 = 0.0 + 24.5t + -24.5t + 4.9t2 + -4.9t2 -8.9 + -24.5t + -4.9t2 = 24.5t + -24.5t + 4.9t2 + -4.9t2 Combine like terms: 24.5t + -24.5t = 0.0 -8.9 + -24.5t + -4.9t2 = 0.0 + 4.9t2 + -4.9t2 -8.9 + -24.5t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 -8.9 + -24.5t + -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'. 1.816326531 + 5t + t2 = 0 Move the constant term to the right: Add '-1.816326531' to each side of the equation. 1.816326531 + 5t + -1.816326531 + t2 = 0 + -1.816326531 Reorder the terms: 1.816326531 + -1.816326531 + 5t + t2 = 0 + -1.816326531 Combine like terms: 1.816326531 + -1.816326531 = 0.000000000 0.000000000 + 5t + t2 = 0 + -1.816326531 5t + t2 = 0 + -1.816326531 Combine like terms: 0 + -1.816326531 = -1.816326531 5t + t2 = -1.816326531 The t term is 5t. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5t + 6.25 + t2 = -1.816326531 + 6.25 Reorder the terms: 6.25 + 5t + t2 = -1.816326531 + 6.25 Combine like terms: -1.816326531 + 6.25 = 4.433673469 6.25 + 5t + t2 = 4.433673469 Factor a perfect square on the left side: (t + 2.5)(t + 2.5) = 4.433673469 Calculate the square root of the right side: 2.105628996 Break this problem into two subproblems by setting (t + 2.5) equal to 2.105628996 and -2.105628996.Subproblem 1
t + 2.5 = 2.105628996 Simplifying t + 2.5 = 2.105628996 Reorder the terms: 2.5 + t = 2.105628996 Solving 2.5 + t = 2.105628996 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + t = 2.105628996 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + t = 2.105628996 + -2.5 t = 2.105628996 + -2.5 Combine like terms: 2.105628996 + -2.5 = -0.394371004 t = -0.394371004 Simplifying t = -0.394371004Subproblem 2
t + 2.5 = -2.105628996 Simplifying t + 2.5 = -2.105628996 Reorder the terms: 2.5 + t = -2.105628996 Solving 2.5 + t = -2.105628996 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + t = -2.105628996 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + t = -2.105628996 + -2.5 t = -2.105628996 + -2.5 Combine like terms: -2.105628996 + -2.5 = -4.605628996 t = -4.605628996 Simplifying t = -4.605628996Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.394371004, -4.605628996}
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