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Simplifying -0.8t2 + 14.4t + 2 = 54 Reorder the terms: 2 + 14.4t + -0.8t2 = 54 Solving 2 + 14.4t + -0.8t2 = 54 Solving for variable 't'. Reorder the terms: 2 + -54 + 14.4t + -0.8t2 = 54 + -54 Combine like terms: 2 + -54 = -52 -52 + 14.4t + -0.8t2 = 54 + -54 Combine like terms: 54 + -54 = 0 -52 + 14.4t + -0.8t2 = 0 Begin completing the square. Divide all terms by -0.8 the coefficient of the squared term: Divide each side by '-0.8'. 65 + -18t + t2 = 0 Move the constant term to the right: Add '-65' to each side of the equation. 65 + -18t + -65 + t2 = 0 + -65 Reorder the terms: 65 + -65 + -18t + t2 = 0 + -65 Combine like terms: 65 + -65 = 0 0 + -18t + t2 = 0 + -65 -18t + t2 = 0 + -65 Combine like terms: 0 + -65 = -65 -18t + t2 = -65 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 = -65 + 81 Reorder the terms: 81 + -18t + t2 = -65 + 81 Combine like terms: -65 + 81 = 16 81 + -18t + t2 = 16 Factor a perfect square on the left side: (t + -9)(t + -9) = 16 Calculate the square root of the right side: 4 Break this problem into two subproblems by setting (t + -9) equal to 4 and -4.Subproblem 1
t + -9 = 4 Simplifying t + -9 = 4 Reorder the terms: -9 + t = 4 Solving -9 + t = 4 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 = 4 + 9 Combine like terms: -9 + 9 = 0 0 + t = 4 + 9 t = 4 + 9 Combine like terms: 4 + 9 = 13 t = 13 Simplifying t = 13Subproblem 2
t + -9 = -4 Simplifying t + -9 = -4 Reorder the terms: -9 + t = -4 Solving -9 + t = -4 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 = -4 + 9 Combine like terms: -9 + 9 = 0 0 + t = -4 + 9 t = -4 + 9 Combine like terms: -4 + 9 = 5 t = 5 Simplifying t = 5Solution
The solution to the problem is based on the solutions from the subproblems. t = {13, 5}
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