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Simplifying 98 = 44.1t + 0.5 * -9.8t * t Multiply 0.5 * -9.8 98 = 44.1t + -4.9t * t Multiply t * t 98 = 44.1t + -4.9t2 Solving 98 = 44.1t + -4.9t2 Solving for variable 't'. Reorder the terms: 98 + -44.1t + 4.9t2 = 44.1t + -44.1t + -4.9t2 + 4.9t2 Combine like terms: 44.1t + -44.1t = 0.0 98 + -44.1t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 98 + -44.1t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 98 + -44.1t + 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'. 20 + -9t + t2 = 0 Move the constant term to the right: Add '-20' to each side of the equation. 20 + -9t + -20 + t2 = 0 + -20 Reorder the terms: 20 + -20 + -9t + t2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -9t + t2 = 0 + -20 -9t + t2 = 0 + -20 Combine like terms: 0 + -20 = -20 -9t + t2 = -20 The t term is -9t. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9t + 20.25 + t2 = -20 + 20.25 Reorder the terms: 20.25 + -9t + t2 = -20 + 20.25 Combine like terms: -20 + 20.25 = 0.25 20.25 + -9t + t2 = 0.25 Factor a perfect square on the left side: (t + -4.5)(t + -4.5) = 0.25 Calculate the square root of the right side: 0.5 Break this problem into two subproblems by setting (t + -4.5) equal to 0.5 and -0.5.Subproblem 1
t + -4.5 = 0.5 Simplifying t + -4.5 = 0.5 Reorder the terms: -4.5 + t = 0.5 Solving -4.5 + t = 0.5 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + t = 0.5 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + t = 0.5 + 4.5 t = 0.5 + 4.5 Combine like terms: 0.5 + 4.5 = 5 t = 5 Simplifying t = 5Subproblem 2
t + -4.5 = -0.5 Simplifying t + -4.5 = -0.5 Reorder the terms: -4.5 + t = -0.5 Solving -4.5 + t = -0.5 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + t = -0.5 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + t = -0.5 + 4.5 t = -0.5 + 4.5 Combine like terms: -0.5 + 4.5 = 4 t = 4 Simplifying t = 4Solution
The solution to the problem is based on the solutions from the subproblems. t = {5, 4}
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