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Simplifying -30 = 15t + -2t2 Solving -30 = 15t + -2t2 Solving for variable 't'. Reorder the terms: -30 + -15t + 2t2 = 15t + -15t + -2t2 + 2t2 Combine like terms: 15t + -15t = 0 -30 + -15t + 2t2 = 0 + -2t2 + 2t2 -30 + -15t + 2t2 = -2t2 + 2t2 Combine like terms: -2t2 + 2t2 = 0 -30 + -15t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -15 + -7.5t + t2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + -7.5t + 15 + t2 = 0 + 15 Reorder the terms: -15 + 15 + -7.5t + t2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -7.5t + t2 = 0 + 15 -7.5t + t2 = 0 + 15 Combine like terms: 0 + 15 = 15 -7.5t + t2 = 15 The t term is -7.5t. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5t + 14.0625 + t2 = 15 + 14.0625 Reorder the terms: 14.0625 + -7.5t + t2 = 15 + 14.0625 Combine like terms: 15 + 14.0625 = 29.0625 14.0625 + -7.5t + t2 = 29.0625 Factor a perfect square on the left side: (t + -3.75)(t + -3.75) = 29.0625 Calculate the square root of the right side: 5.390964663 Break this problem into two subproblems by setting (t + -3.75) equal to 5.390964663 and -5.390964663.Subproblem 1
t + -3.75 = 5.390964663 Simplifying t + -3.75 = 5.390964663 Reorder the terms: -3.75 + t = 5.390964663 Solving -3.75 + t = 5.390964663 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + t = 5.390964663 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + t = 5.390964663 + 3.75 t = 5.390964663 + 3.75 Combine like terms: 5.390964663 + 3.75 = 9.140964663 t = 9.140964663 Simplifying t = 9.140964663Subproblem 2
t + -3.75 = -5.390964663 Simplifying t + -3.75 = -5.390964663 Reorder the terms: -3.75 + t = -5.390964663 Solving -3.75 + t = -5.390964663 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + t = -5.390964663 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + t = -5.390964663 + 3.75 t = -5.390964663 + 3.75 Combine like terms: -5.390964663 + 3.75 = -1.640964663 t = -1.640964663 Simplifying t = -1.640964663Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.140964663, -1.640964663}
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