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Simplifying -98 = 4.9t(8 + -1t) -98 = (8 * 4.9t + -1t * 4.9t) -98 = (39.2t + -4.9t2) Solving -98 = 39.2t + -4.9t2 Solving for variable 't'. Reorder the terms: -98 + -39.2t + 4.9t2 = 39.2t + -39.2t + -4.9t2 + 4.9t2 Combine like terms: 39.2t + -39.2t = 0.0 -98 + -39.2t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 -98 + -39.2t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -98 + -39.2t + 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 + -8t + t2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -8t + 20 + t2 = 0 + 20 Reorder the terms: -20 + 20 + -8t + t2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -8t + t2 = 0 + 20 -8t + t2 = 0 + 20 Combine like terms: 0 + 20 = 20 -8t + t2 = 20 The t term is -8t. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8t + 16 + t2 = 20 + 16 Reorder the terms: 16 + -8t + t2 = 20 + 16 Combine like terms: 20 + 16 = 36 16 + -8t + t2 = 36 Factor a perfect square on the left side: (t + -4)(t + -4) = 36 Calculate the square root of the right side: 6 Break this problem into two subproblems by setting (t + -4) equal to 6 and -6.Subproblem 1
t + -4 = 6 Simplifying t + -4 = 6 Reorder the terms: -4 + t = 6 Solving -4 + t = 6 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = 6 + 4 Combine like terms: -4 + 4 = 0 0 + t = 6 + 4 t = 6 + 4 Combine like terms: 6 + 4 = 10 t = 10 Simplifying t = 10Subproblem 2
t + -4 = -6 Simplifying t + -4 = -6 Reorder the terms: -4 + t = -6 Solving -4 + t = -6 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = -6 + 4 Combine like terms: -4 + 4 = 0 0 + t = -6 + 4 t = -6 + 4 Combine like terms: -6 + 4 = -2 t = -2 Simplifying t = -2Solution
The solution to the problem is based on the solutions from the subproblems. t = {10, -2}
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