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Simplifying 27 = 60t + -5t2 Solving 27 = 60t + -5t2 Solving for variable 't'. Reorder the terms: 27 + -60t + 5t2 = 60t + -60t + -5t2 + 5t2 Combine like terms: 60t + -60t = 0 27 + -60t + 5t2 = 0 + -5t2 + 5t2 27 + -60t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 27 + -60t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 5.4 + -12t + t2 = 0 Move the constant term to the right: Add '-5.4' to each side of the equation. 5.4 + -12t + -5.4 + t2 = 0 + -5.4 Reorder the terms: 5.4 + -5.4 + -12t + t2 = 0 + -5.4 Combine like terms: 5.4 + -5.4 = 0.0 0.0 + -12t + t2 = 0 + -5.4 -12t + t2 = 0 + -5.4 Combine like terms: 0 + -5.4 = -5.4 -12t + t2 = -5.4 The t term is -12t. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12t + 36 + t2 = -5.4 + 36 Reorder the terms: 36 + -12t + t2 = -5.4 + 36 Combine like terms: -5.4 + 36 = 30.6 36 + -12t + t2 = 30.6 Factor a perfect square on the left side: (t + -6)(t + -6) = 30.6 Calculate the square root of the right side: 5.531726674 Break this problem into two subproblems by setting (t + -6) equal to 5.531726674 and -5.531726674.Subproblem 1
t + -6 = 5.531726674 Simplifying t + -6 = 5.531726674 Reorder the terms: -6 + t = 5.531726674 Solving -6 + t = 5.531726674 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + t = 5.531726674 + 6 Combine like terms: -6 + 6 = 0 0 + t = 5.531726674 + 6 t = 5.531726674 + 6 Combine like terms: 5.531726674 + 6 = 11.531726674 t = 11.531726674 Simplifying t = 11.531726674Subproblem 2
t + -6 = -5.531726674 Simplifying t + -6 = -5.531726674 Reorder the terms: -6 + t = -5.531726674 Solving -6 + t = -5.531726674 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + t = -5.531726674 + 6 Combine like terms: -6 + 6 = 0 0 + t = -5.531726674 + 6 t = -5.531726674 + 6 Combine like terms: -5.531726674 + 6 = 0.468273326 t = 0.468273326 Simplifying t = 0.468273326Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.531726674, 0.468273326}
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