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Simplifying 5 = -3t2 + 36t Reorder the terms: 5 = 36t + -3t2 Solving 5 = 36t + -3t2 Solving for variable 't'. Reorder the terms: 5 + -36t + 3t2 = 36t + -36t + -3t2 + 3t2 Combine like terms: 36t + -36t = 0 5 + -36t + 3t2 = 0 + -3t2 + 3t2 5 + -36t + 3t2 = -3t2 + 3t2 Combine like terms: -3t2 + 3t2 = 0 5 + -36t + 3t2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.666666667 + -12t + t2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + -12t + -1.666666667 + t2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + -12t + t2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + -12t + t2 = 0 + -1.666666667 -12t + t2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 -12t + t2 = -1.666666667 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 = -1.666666667 + 36 Reorder the terms: 36 + -12t + t2 = -1.666666667 + 36 Combine like terms: -1.666666667 + 36 = 34.333333333 36 + -12t + t2 = 34.333333333 Factor a perfect square on the left side: (t + -6)(t + -6) = 34.333333333 Calculate the square root of the right side: 5.859465277 Break this problem into two subproblems by setting (t + -6) equal to 5.859465277 and -5.859465277.Subproblem 1
t + -6 = 5.859465277 Simplifying t + -6 = 5.859465277 Reorder the terms: -6 + t = 5.859465277 Solving -6 + t = 5.859465277 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 = 5.859465277 + 6 Combine like terms: -6 + 6 = 0 0 + t = 5.859465277 + 6 t = 5.859465277 + 6 Combine like terms: 5.859465277 + 6 = 11.859465277 t = 11.859465277 Simplifying t = 11.859465277Subproblem 2
t + -6 = -5.859465277 Simplifying t + -6 = -5.859465277 Reorder the terms: -6 + t = -5.859465277 Solving -6 + t = -5.859465277 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 = -5.859465277 + 6 Combine like terms: -6 + 6 = 0 0 + t = -5.859465277 + 6 t = -5.859465277 + 6 Combine like terms: -5.859465277 + 6 = 0.140534723 t = 0.140534723 Simplifying t = 0.140534723Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.859465277, 0.140534723}
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