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Simplifying 36 = -4.5t2 + 27t Reorder the terms: 36 = 27t + -4.5t2 Solving 36 = 27t + -4.5t2 Solving for variable 't'. Reorder the terms: 36 + -27t + 4.5t2 = 27t + -27t + -4.5t2 + 4.5t2 Combine like terms: 27t + -27t = 0 36 + -27t + 4.5t2 = 0 + -4.5t2 + 4.5t2 36 + -27t + 4.5t2 = -4.5t2 + 4.5t2 Combine like terms: -4.5t2 + 4.5t2 = 0.0 36 + -27t + 4.5t2 = 0.0 Begin completing the square. Divide all terms by 4.5 the coefficient of the squared term: Divide each side by '4.5'. 8 + -6t + t2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + -6t + -8 + t2 = 0 + -8 Reorder the terms: 8 + -8 + -6t + t2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -6t + t2 = 0 + -8 -6t + t2 = 0 + -8 Combine like terms: 0 + -8 = -8 -6t + t2 = -8 The t term is -6t. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6t + 9 + t2 = -8 + 9 Reorder the terms: 9 + -6t + t2 = -8 + 9 Combine like terms: -8 + 9 = 1 9 + -6t + t2 = 1 Factor a perfect square on the left side: (t + -3)(t + -3) = 1 Calculate the square root of the right side: 1 Break this problem into two subproblems by setting (t + -3) equal to 1 and -1.Subproblem 1
t + -3 = 1 Simplifying t + -3 = 1 Reorder the terms: -3 + t = 1 Solving -3 + t = 1 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = 1 + 3 Combine like terms: -3 + 3 = 0 0 + t = 1 + 3 t = 1 + 3 Combine like terms: 1 + 3 = 4 t = 4 Simplifying t = 4Subproblem 2
t + -3 = -1 Simplifying t + -3 = -1 Reorder the terms: -3 + t = -1 Solving -3 + t = -1 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = -1 + 3 Combine like terms: -3 + 3 = 0 0 + t = -1 + 3 t = -1 + 3 Combine like terms: -1 + 3 = 2 t = 2 Simplifying t = 2Solution
The solution to the problem is based on the solutions from the subproblems. t = {4, 2}
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