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Simplifying 0 = -0.8t2 + 14.4t + 2 Reorder the terms: 0 = 2 + 14.4t + -0.8t2 Solving 0 = 2 + 14.4t + -0.8t2 Solving for variable 't'. Combine like terms: 0 + -2 = -2 -2 + -14.4t + 0.8t2 = 2 + 14.4t + -0.8t2 + -2 + -14.4t + 0.8t2 Reorder the terms: -2 + -14.4t + 0.8t2 = 2 + -2 + 14.4t + -14.4t + -0.8t2 + 0.8t2 Combine like terms: 2 + -2 = 0 -2 + -14.4t + 0.8t2 = 0 + 14.4t + -14.4t + -0.8t2 + 0.8t2 -2 + -14.4t + 0.8t2 = 14.4t + -14.4t + -0.8t2 + 0.8t2 Combine like terms: 14.4t + -14.4t = 0.0 -2 + -14.4t + 0.8t2 = 0.0 + -0.8t2 + 0.8t2 -2 + -14.4t + 0.8t2 = -0.8t2 + 0.8t2 Combine like terms: -0.8t2 + 0.8t2 = 0.0 -2 + -14.4t + 0.8t2 = 0.0 Begin completing the square. Divide all terms by 0.8 the coefficient of the squared term: Divide each side by '0.8'. -2.5 + -18t + t2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -18t + 2.5 + t2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -18t + t2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -18t + t2 = 0 + 2.5 -18t + t2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -18t + t2 = 2.5 The t term is -18t. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18t + 81 + t2 = 2.5 + 81 Reorder the terms: 81 + -18t + t2 = 2.5 + 81 Combine like terms: 2.5 + 81 = 83.5 81 + -18t + t2 = 83.5 Factor a perfect square on the left side: (t + -9)(t + -9) = 83.5 Calculate the square root of the right side: 9.137833441 Break this problem into two subproblems by setting (t + -9) equal to 9.137833441 and -9.137833441.Subproblem 1
t + -9 = 9.137833441 Simplifying t + -9 = 9.137833441 Reorder the terms: -9 + t = 9.137833441 Solving -9 + t = 9.137833441 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + t = 9.137833441 + 9 Combine like terms: -9 + 9 = 0 0 + t = 9.137833441 + 9 t = 9.137833441 + 9 Combine like terms: 9.137833441 + 9 = 18.137833441 t = 18.137833441 Simplifying t = 18.137833441Subproblem 2
t + -9 = -9.137833441 Simplifying t + -9 = -9.137833441 Reorder the terms: -9 + t = -9.137833441 Solving -9 + t = -9.137833441 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + t = -9.137833441 + 9 Combine like terms: -9 + 9 = 0 0 + t = -9.137833441 + 9 t = -9.137833441 + 9 Combine like terms: -9.137833441 + 9 = -0.137833441 t = -0.137833441 Simplifying t = -0.137833441Solution
The solution to the problem is based on the solutions from the subproblems. t = {18.137833441, -0.137833441}
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