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Simplifying 2t2 + -15t + -6 = 0 Reorder the terms: -6 + -15t + 2t2 = 0 Solving -6 + -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'. -3 + -7.5t + t2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -7.5t + 3 + t2 = 0 + 3 Reorder the terms: -3 + 3 + -7.5t + t2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -7.5t + t2 = 0 + 3 -7.5t + t2 = 0 + 3 Combine like terms: 0 + 3 = 3 -7.5t + t2 = 3 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 = 3 + 14.0625 Reorder the terms: 14.0625 + -7.5t + t2 = 3 + 14.0625 Combine like terms: 3 + 14.0625 = 17.0625 14.0625 + -7.5t + t2 = 17.0625 Factor a perfect square on the left side: (t + -3.75)(t + -3.75) = 17.0625 Calculate the square root of the right side: 4.13067791 Break this problem into two subproblems by setting (t + -3.75) equal to 4.13067791 and -4.13067791.Subproblem 1
t + -3.75 = 4.13067791 Simplifying t + -3.75 = 4.13067791 Reorder the terms: -3.75 + t = 4.13067791 Solving -3.75 + t = 4.13067791 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 = 4.13067791 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + t = 4.13067791 + 3.75 t = 4.13067791 + 3.75 Combine like terms: 4.13067791 + 3.75 = 7.88067791 t = 7.88067791 Simplifying t = 7.88067791Subproblem 2
t + -3.75 = -4.13067791 Simplifying t + -3.75 = -4.13067791 Reorder the terms: -3.75 + t = -4.13067791 Solving -3.75 + t = -4.13067791 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 = -4.13067791 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + t = -4.13067791 + 3.75 t = -4.13067791 + 3.75 Combine like terms: -4.13067791 + 3.75 = -0.38067791 t = -0.38067791 Simplifying t = -0.38067791Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.88067791, -0.38067791}
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