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Simplifying 15t + 2t2 + -18 = 0 Reorder the terms: -18 + 15t + 2t2 = 0 Solving -18 + 15t + 2t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -9 + 7.5t + t2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 7.5t + 9 + t2 = 0 + 9 Reorder the terms: -9 + 9 + 7.5t + t2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 7.5t + t2 = 0 + 9 7.5t + t2 = 0 + 9 Combine like terms: 0 + 9 = 9 7.5t + t2 = 9 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 = 9 + 14.0625 Reorder the terms: 14.0625 + 7.5t + t2 = 9 + 14.0625 Combine like terms: 9 + 14.0625 = 23.0625 14.0625 + 7.5t + t2 = 23.0625 Factor a perfect square on the left side: (t + 3.75)(t + 3.75) = 23.0625 Calculate the square root of the right side: 4.802343178 Break this problem into two subproblems by setting (t + 3.75) equal to 4.802343178 and -4.802343178.Subproblem 1
t + 3.75 = 4.802343178 Simplifying t + 3.75 = 4.802343178 Reorder the terms: 3.75 + t = 4.802343178 Solving 3.75 + t = 4.802343178 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 = 4.802343178 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + t = 4.802343178 + -3.75 t = 4.802343178 + -3.75 Combine like terms: 4.802343178 + -3.75 = 1.052343178 t = 1.052343178 Simplifying t = 1.052343178Subproblem 2
t + 3.75 = -4.802343178 Simplifying t + 3.75 = -4.802343178 Reorder the terms: 3.75 + t = -4.802343178 Solving 3.75 + t = -4.802343178 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 = -4.802343178 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + t = -4.802343178 + -3.75 t = -4.802343178 + -3.75 Combine like terms: -4.802343178 + -3.75 = -8.552343178 t = -8.552343178 Simplifying t = -8.552343178Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.052343178, -8.552343178}
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