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Simplifying 1.5t2 + 12t + -52 = 0 Reorder the terms: -52 + 12t + 1.5t2 = 0 Solving -52 + 12t + 1.5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 1.5 the coefficient of the squared term: Divide each side by '1.5'. -34.66666667 + 8t + t2 = 0 Move the constant term to the right: Add '34.66666667' to each side of the equation. -34.66666667 + 8t + 34.66666667 + t2 = 0 + 34.66666667 Reorder the terms: -34.66666667 + 34.66666667 + 8t + t2 = 0 + 34.66666667 Combine like terms: -34.66666667 + 34.66666667 = 0.00000000 0.00000000 + 8t + t2 = 0 + 34.66666667 8t + t2 = 0 + 34.66666667 Combine like terms: 0 + 34.66666667 = 34.66666667 8t + t2 = 34.66666667 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 = 34.66666667 + 16 Reorder the terms: 16 + 8t + t2 = 34.66666667 + 16 Combine like terms: 34.66666667 + 16 = 50.66666667 16 + 8t + t2 = 50.66666667 Factor a perfect square on the left side: (t + 4)(t + 4) = 50.66666667 Calculate the square root of the right side: 7.118052168 Break this problem into two subproblems by setting (t + 4) equal to 7.118052168 and -7.118052168.Subproblem 1
t + 4 = 7.118052168 Simplifying t + 4 = 7.118052168 Reorder the terms: 4 + t = 7.118052168 Solving 4 + t = 7.118052168 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 = 7.118052168 + -4 Combine like terms: 4 + -4 = 0 0 + t = 7.118052168 + -4 t = 7.118052168 + -4 Combine like terms: 7.118052168 + -4 = 3.118052168 t = 3.118052168 Simplifying t = 3.118052168Subproblem 2
t + 4 = -7.118052168 Simplifying t + 4 = -7.118052168 Reorder the terms: 4 + t = -7.118052168 Solving 4 + t = -7.118052168 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 = -7.118052168 + -4 Combine like terms: 4 + -4 = 0 0 + t = -7.118052168 + -4 t = -7.118052168 + -4 Combine like terms: -7.118052168 + -4 = -11.118052168 t = -11.118052168 Simplifying t = -11.118052168Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.118052168, -11.118052168}
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