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Simplifying -5t2 + 35t + -6 = 0 Reorder the terms: -6 + 35t + -5t2 = 0 Solving -6 + 35t + -5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 1.2 + -7t + t2 = 0 Move the constant term to the right: Add '-1.2' to each side of the equation. 1.2 + -7t + -1.2 + t2 = 0 + -1.2 Reorder the terms: 1.2 + -1.2 + -7t + t2 = 0 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + -7t + t2 = 0 + -1.2 -7t + t2 = 0 + -1.2 Combine like terms: 0 + -1.2 = -1.2 -7t + t2 = -1.2 The t term is -7t. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7t + 12.25 + t2 = -1.2 + 12.25 Reorder the terms: 12.25 + -7t + t2 = -1.2 + 12.25 Combine like terms: -1.2 + 12.25 = 11.05 12.25 + -7t + t2 = 11.05 Factor a perfect square on the left side: (t + -3.5)(t + -3.5) = 11.05 Calculate the square root of the right side: 3.324154028 Break this problem into two subproblems by setting (t + -3.5) equal to 3.324154028 and -3.324154028.Subproblem 1
t + -3.5 = 3.324154028 Simplifying t + -3.5 = 3.324154028 Reorder the terms: -3.5 + t = 3.324154028 Solving -3.5 + t = 3.324154028 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + t = 3.324154028 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = 3.324154028 + 3.5 t = 3.324154028 + 3.5 Combine like terms: 3.324154028 + 3.5 = 6.824154028 t = 6.824154028 Simplifying t = 6.824154028Subproblem 2
t + -3.5 = -3.324154028 Simplifying t + -3.5 = -3.324154028 Reorder the terms: -3.5 + t = -3.324154028 Solving -3.5 + t = -3.324154028 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + t = -3.324154028 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = -3.324154028 + 3.5 t = -3.324154028 + 3.5 Combine like terms: -3.324154028 + 3.5 = 0.175845972 t = 0.175845972 Simplifying t = 0.175845972Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.824154028, 0.175845972}
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