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Simplifying 120 = 18t + -0.6t2 Solving 120 = 18t + -0.6t2 Solving for variable 't'. Reorder the terms: 120 + -18t + 0.6t2 = 18t + -18t + -0.6t2 + 0.6t2 Combine like terms: 18t + -18t = 0 120 + -18t + 0.6t2 = 0 + -0.6t2 + 0.6t2 120 + -18t + 0.6t2 = -0.6t2 + 0.6t2 Combine like terms: -0.6t2 + 0.6t2 = 0.0 120 + -18t + 0.6t2 = 0.0 Begin completing the square. Divide all terms by 0.6 the coefficient of the squared term: Divide each side by '0.6'. 200 + -30t + t2 = 0 Move the constant term to the right: Add '-200' to each side of the equation. 200 + -30t + -200 + t2 = 0 + -200 Reorder the terms: 200 + -200 + -30t + t2 = 0 + -200 Combine like terms: 200 + -200 = 0 0 + -30t + t2 = 0 + -200 -30t + t2 = 0 + -200 Combine like terms: 0 + -200 = -200 -30t + t2 = -200 The t term is -30t. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30t + 225 + t2 = -200 + 225 Reorder the terms: 225 + -30t + t2 = -200 + 225 Combine like terms: -200 + 225 = 25 225 + -30t + t2 = 25 Factor a perfect square on the left side: (t + -15)(t + -15) = 25 Calculate the square root of the right side: 5 Break this problem into two subproblems by setting (t + -15) equal to 5 and -5.Subproblem 1
t + -15 = 5 Simplifying t + -15 = 5 Reorder the terms: -15 + t = 5 Solving -15 + t = 5 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + t = 5 + 15 Combine like terms: -15 + 15 = 0 0 + t = 5 + 15 t = 5 + 15 Combine like terms: 5 + 15 = 20 t = 20 Simplifying t = 20Subproblem 2
t + -15 = -5 Simplifying t + -15 = -5 Reorder the terms: -15 + t = -5 Solving -15 + t = -5 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + t = -5 + 15 Combine like terms: -15 + 15 = 0 0 + t = -5 + 15 t = -5 + 15 Combine like terms: -5 + 15 = 10 t = 10 Simplifying t = 10Solution
The solution to the problem is based on the solutions from the subproblems. t = {20, 10}
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