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Simplifying -5t2 + 40t + 1.2 = 60 Reorder the terms: 1.2 + 40t + -5t2 = 60 Solving 1.2 + 40t + -5t2 = 60 Solving for variable 't'. Reorder the terms: 1.2 + -60 + 40t + -5t2 = 60 + -60 Combine like terms: 1.2 + -60 = -58.8 -58.8 + 40t + -5t2 = 60 + -60 Combine like terms: 60 + -60 = 0 -58.8 + 40t + -5t2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 11.76 + -8t + t2 = 0 Move the constant term to the right: Add '-11.76' to each side of the equation. 11.76 + -8t + -11.76 + t2 = 0 + -11.76 Reorder the terms: 11.76 + -11.76 + -8t + t2 = 0 + -11.76 Combine like terms: 11.76 + -11.76 = 0.00 0.00 + -8t + t2 = 0 + -11.76 -8t + t2 = 0 + -11.76 Combine like terms: 0 + -11.76 = -11.76 -8t + t2 = -11.76 The t term is -8t. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8t + 16 + t2 = -11.76 + 16 Reorder the terms: 16 + -8t + t2 = -11.76 + 16 Combine like terms: -11.76 + 16 = 4.24 16 + -8t + t2 = 4.24 Factor a perfect square on the left side: (t + -4)(t + -4) = 4.24 Calculate the square root of the right side: 2.059126028 Break this problem into two subproblems by setting (t + -4) equal to 2.059126028 and -2.059126028.Subproblem 1
t + -4 = 2.059126028 Simplifying t + -4 = 2.059126028 Reorder the terms: -4 + t = 2.059126028 Solving -4 + t = 2.059126028 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = 2.059126028 + 4 Combine like terms: -4 + 4 = 0 0 + t = 2.059126028 + 4 t = 2.059126028 + 4 Combine like terms: 2.059126028 + 4 = 6.059126028 t = 6.059126028 Simplifying t = 6.059126028Subproblem 2
t + -4 = -2.059126028 Simplifying t + -4 = -2.059126028 Reorder the terms: -4 + t = -2.059126028 Solving -4 + t = -2.059126028 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = -2.059126028 + 4 Combine like terms: -4 + 4 = 0 0 + t = -2.059126028 + 4 t = -2.059126028 + 4 Combine like terms: -2.059126028 + 4 = 1.940873972 t = 1.940873972 Simplifying t = 1.940873972Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.059126028, 1.940873972}
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