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Simplifying -16t2 + 75t + 5 = 0 Reorder the terms: 5 + 75t + -16t2 = 0 Solving 5 + 75t + -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 + -4.6875t + t2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -4.6875t + 0.3125 + t2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -4.6875t + t2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -4.6875t + t2 = 0 + 0.3125 -4.6875t + t2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -4.6875t + t2 = 0.3125 The t term is -4.6875t. Take half its coefficient (-2.34375). Square it (5.493164063) and add it to both sides. Add '5.493164063' to each side of the equation. -4.6875t + 5.493164063 + t2 = 0.3125 + 5.493164063 Reorder the terms: 5.493164063 + -4.6875t + t2 = 0.3125 + 5.493164063 Combine like terms: 0.3125 + 5.493164063 = 5.805664063 5.493164063 + -4.6875t + t2 = 5.805664063 Factor a perfect square on the left side: (t + -2.34375)(t + -2.34375) = 5.805664063 Calculate the square root of the right side: 2.409494566 Break this problem into two subproblems by setting (t + -2.34375) equal to 2.409494566 and -2.409494566.Subproblem 1
t + -2.34375 = 2.409494566 Simplifying t + -2.34375 = 2.409494566 Reorder the terms: -2.34375 + t = 2.409494566 Solving -2.34375 + t = 2.409494566 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.34375' to each side of the equation. -2.34375 + 2.34375 + t = 2.409494566 + 2.34375 Combine like terms: -2.34375 + 2.34375 = 0.00000 0.00000 + t = 2.409494566 + 2.34375 t = 2.409494566 + 2.34375 Combine like terms: 2.409494566 + 2.34375 = 4.753244566 t = 4.753244566 Simplifying t = 4.753244566Subproblem 2
t + -2.34375 = -2.409494566 Simplifying t + -2.34375 = -2.409494566 Reorder the terms: -2.34375 + t = -2.409494566 Solving -2.34375 + t = -2.409494566 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.34375' to each side of the equation. -2.34375 + 2.34375 + t = -2.409494566 + 2.34375 Combine like terms: -2.34375 + 2.34375 = 0.00000 0.00000 + t = -2.409494566 + 2.34375 t = -2.409494566 + 2.34375 Combine like terms: -2.409494566 + 2.34375 = -0.065744566 t = -0.065744566 Simplifying t = -0.065744566Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.753244566, -0.065744566}
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