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Simplifying -4.9t2 + 9.8t + 73.5 = 0 Reorder the terms: 73.5 + 9.8t + -4.9t2 = 0 Solving 73.5 + 9.8t + -4.9t2 = 0 Solving for variable 't'. 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 = 5 t = 5 Simplifying t = 5Subproblem 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 = -3 t = -3 Simplifying t = -3Solution
The solution to the problem is based on the solutions from the subproblems. t = {5, -3}
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