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Simplifying 0 = -4.9t2 + 36t + 24 Reorder the terms: 0 = 24 + 36t + -4.9t2 Solving 0 = 24 + 36t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -24 = -24 -24 + -36t + 4.9t2 = 24 + 36t + -4.9t2 + -24 + -36t + 4.9t2 Reorder the terms: -24 + -36t + 4.9t2 = 24 + -24 + 36t + -36t + -4.9t2 + 4.9t2 Combine like terms: 24 + -24 = 0 -24 + -36t + 4.9t2 = 0 + 36t + -36t + -4.9t2 + 4.9t2 -24 + -36t + 4.9t2 = 36t + -36t + -4.9t2 + 4.9t2 Combine like terms: 36t + -36t = 0 -24 + -36t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -24 + -36t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -24 + -36t + 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'. -4.897959184 + -7.346938776t + t2 = 0 Move the constant term to the right: Add '4.897959184' to each side of the equation. -4.897959184 + -7.346938776t + 4.897959184 + t2 = 0 + 4.897959184 Reorder the terms: -4.897959184 + 4.897959184 + -7.346938776t + t2 = 0 + 4.897959184 Combine like terms: -4.897959184 + 4.897959184 = 0.000000000 0.000000000 + -7.346938776t + t2 = 0 + 4.897959184 -7.346938776t + t2 = 0 + 4.897959184 Combine like terms: 0 + 4.897959184 = 4.897959184 -7.346938776t + t2 = 4.897959184 The t term is -7.346938776t. Take half its coefficient (-3.673469388). Square it (13.49437734) and add it to both sides. Add '13.49437734' to each side of the equation. -7.346938776t + 13.49437734 + t2 = 4.897959184 + 13.49437734 Reorder the terms: 13.49437734 + -7.346938776t + t2 = 4.897959184 + 13.49437734 Combine like terms: 4.897959184 + 13.49437734 = 18.392336524 13.49437734 + -7.346938776t + t2 = 18.392336524 Factor a perfect square on the left side: (t + -3.673469388)(t + -3.673469388) = 18.392336524 Calculate the square root of the right side: 4.288628746 Break this problem into two subproblems by setting (t + -3.673469388) equal to 4.288628746 and -4.288628746.Subproblem 1
t + -3.673469388 = 4.288628746 Simplifying t + -3.673469388 = 4.288628746 Reorder the terms: -3.673469388 + t = 4.288628746 Solving -3.673469388 + t = 4.288628746 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.673469388' to each side of the equation. -3.673469388 + 3.673469388 + t = 4.288628746 + 3.673469388 Combine like terms: -3.673469388 + 3.673469388 = 0.000000000 0.000000000 + t = 4.288628746 + 3.673469388 t = 4.288628746 + 3.673469388 Combine like terms: 4.288628746 + 3.673469388 = 7.962098134 t = 7.962098134 Simplifying t = 7.962098134Subproblem 2
t + -3.673469388 = -4.288628746 Simplifying t + -3.673469388 = -4.288628746 Reorder the terms: -3.673469388 + t = -4.288628746 Solving -3.673469388 + t = -4.288628746 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.673469388' to each side of the equation. -3.673469388 + 3.673469388 + t = -4.288628746 + 3.673469388 Combine like terms: -3.673469388 + 3.673469388 = 0.000000000 0.000000000 + t = -4.288628746 + 3.673469388 t = -4.288628746 + 3.673469388 Combine like terms: -4.288628746 + 3.673469388 = -0.615159358 t = -0.615159358 Simplifying t = -0.615159358Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.962098134, -0.615159358}
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