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Simplifying 73.5 = 9.8t + 4.9t2 Solving 73.5 = 9.8t + 4.9t2 Solving for variable 't'. Reorder the terms: 73.5 + -9.8t + -4.9t2 = 9.8t + -9.8t + 4.9t2 + -4.9t2 Combine like terms: 9.8t + -9.8t = 0.0 73.5 + -9.8t + -4.9t2 = 0.0 + 4.9t2 + -4.9t2 73.5 + -9.8t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 73.5 + -9.8t + -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 + 2t + t2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + 2t + 15 + t2 = 0 + 15 Reorder the terms: -15 + 15 + 2t + t2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 2t + t2 = 0 + 15 2t + t2 = 0 + 15 Combine like terms: 0 + 15 = 15 2t + t2 = 15 The t term is 2t. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2t + 1 + t2 = 15 + 1 Reorder the terms: 1 + 2t + t2 = 15 + 1 Combine like terms: 15 + 1 = 16 1 + 2t + t2 = 16 Factor a perfect square on the left side: (t + 1)(t + 1) = 16 Calculate the square root of the right side: 4 Break this problem into two subproblems by setting (t + 1) equal to 4 and -4.Subproblem 1
t + 1 = 4 Simplifying t + 1 = 4 Reorder the terms: 1 + t = 4 Solving 1 + t = 4 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = 4 + -1 Combine like terms: 1 + -1 = 0 0 + t = 4 + -1 t = 4 + -1 Combine like terms: 4 + -1 = 3 t = 3 Simplifying t = 3Subproblem 2
t + 1 = -4 Simplifying t + 1 = -4 Reorder the terms: 1 + t = -4 Solving 1 + t = -4 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = -4 + -1 Combine like terms: 1 + -1 = 0 0 + t = -4 + -1 t = -4 + -1 Combine like terms: -4 + -1 = -5 t = -5 Simplifying t = -5Solution
The solution to the problem is based on the solutions from the subproblems. t = {3, -5}
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