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Simplifying 60 = 3.5t + -0.05(t * t) Multiply t * t 60 = 3.5t + -0.05(t2) Solving 60 = 3.5t + -0.05t2 Solving for variable 't'. Reorder the terms: 60 + -3.5t + 0.05t2 = 3.5t + -3.5t + -0.05t2 + 0.05t2 Combine like terms: 3.5t + -3.5t = 0.0 60 + -3.5t + 0.05t2 = 0.0 + -0.05t2 + 0.05t2 60 + -3.5t + 0.05t2 = -0.05t2 + 0.05t2 Combine like terms: -0.05t2 + 0.05t2 = 0.00 60 + -3.5t + 0.05t2 = 0.00 Begin completing the square. Divide all terms by 0.05 the coefficient of the squared term: Divide each side by '0.05'. 1200 + -70t + t2 = 0 Move the constant term to the right: Add '-1200' to each side of the equation. 1200 + -70t + -1200 + t2 = 0 + -1200 Reorder the terms: 1200 + -1200 + -70t + t2 = 0 + -1200 Combine like terms: 1200 + -1200 = 0 0 + -70t + t2 = 0 + -1200 -70t + t2 = 0 + -1200 Combine like terms: 0 + -1200 = -1200 -70t + t2 = -1200 The t term is -70t. Take half its coefficient (-35). Square it (1225) and add it to both sides. Add '1225' to each side of the equation. -70t + 1225 + t2 = -1200 + 1225 Reorder the terms: 1225 + -70t + t2 = -1200 + 1225 Combine like terms: -1200 + 1225 = 25 1225 + -70t + t2 = 25 Factor a perfect square on the left side: (t + -35)(t + -35) = 25 Calculate the square root of the right side: 5 Break this problem into two subproblems by setting (t + -35) equal to 5 and -5.Subproblem 1
t + -35 = 5 Simplifying t + -35 = 5 Reorder the terms: -35 + t = 5 Solving -35 + t = 5 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + t = 5 + 35 Combine like terms: -35 + 35 = 0 0 + t = 5 + 35 t = 5 + 35 Combine like terms: 5 + 35 = 40 t = 40 Simplifying t = 40Subproblem 2
t + -35 = -5 Simplifying t + -35 = -5 Reorder the terms: -35 + t = -5 Solving -35 + t = -5 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + t = -5 + 35 Combine like terms: -35 + 35 = 0 0 + t = -5 + 35 t = -5 + 35 Combine like terms: -5 + 35 = 30 t = 30 Simplifying t = 30Solution
The solution to the problem is based on the solutions from the subproblems. t = {40, 30}
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