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Simplifying -16t2 + 36t + -5 = 0 Reorder the terms: -5 + 36t + -16t2 = 0 Solving -5 + 36t + -16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 0.3125 + -2.25t + t2 = 0 Move the constant term to the right: Add '-0.3125' to each side of the equation. 0.3125 + -2.25t + -0.3125 + t2 = 0 + -0.3125 Reorder the terms: 0.3125 + -0.3125 + -2.25t + t2 = 0 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + -2.25t + t2 = 0 + -0.3125 -2.25t + t2 = 0 + -0.3125 Combine like terms: 0 + -0.3125 = -0.3125 -2.25t + t2 = -0.3125 The t term is -2.25t. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25t + 1.265625 + t2 = -0.3125 + 1.265625 Reorder the terms: 1.265625 + -2.25t + t2 = -0.3125 + 1.265625 Combine like terms: -0.3125 + 1.265625 = 0.953125 1.265625 + -2.25t + t2 = 0.953125 Factor a perfect square on the left side: (t + -1.125)(t + -1.125) = 0.953125 Calculate the square root of the right side: 0.976281209 Break this problem into two subproblems by setting (t + -1.125) equal to 0.976281209 and -0.976281209.Subproblem 1
t + -1.125 = 0.976281209 Simplifying t + -1.125 = 0.976281209 Reorder the terms: -1.125 + t = 0.976281209 Solving -1.125 + t = 0.976281209 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + t = 0.976281209 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + t = 0.976281209 + 1.125 t = 0.976281209 + 1.125 Combine like terms: 0.976281209 + 1.125 = 2.101281209 t = 2.101281209 Simplifying t = 2.101281209Subproblem 2
t + -1.125 = -0.976281209 Simplifying t + -1.125 = -0.976281209 Reorder the terms: -1.125 + t = -0.976281209 Solving -1.125 + t = -0.976281209 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + t = -0.976281209 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + t = -0.976281209 + 1.125 t = -0.976281209 + 1.125 Combine like terms: -0.976281209 + 1.125 = 0.148718791 t = 0.148718791 Simplifying t = 0.148718791Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.101281209, 0.148718791}
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