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Simplifying -16t2 + 17.88854382t + -5 = 0 Reorder the terms: -5 + 17.88854382t + -16t2 = 0 Solving -5 + 17.88854382t + -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 + -1.118033989t + t2 = 0 Move the constant term to the right: Add '-0.3125' to each side of the equation. 0.3125 + -1.118033989t + -0.3125 + t2 = 0 + -0.3125 Reorder the terms: 0.3125 + -0.3125 + -1.118033989t + t2 = 0 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + -1.118033989t + t2 = 0 + -0.3125 -1.118033989t + t2 = 0 + -0.3125 Combine like terms: 0 + -0.3125 = -0.3125 -1.118033989t + t2 = -0.3125 The t term is -1.118033989t. Take half its coefficient (-0.5590169945). Square it (0.3125000001) and add it to both sides. Add '0.3125000001' to each side of the equation. -1.118033989t + 0.3125000001 + t2 = -0.3125 + 0.3125000001 Reorder the terms: 0.3125000001 + -1.118033989t + t2 = -0.3125 + 0.3125000001 Combine like terms: -0.3125 + 0.3125000001 = 0.0000000001 0.3125000001 + -1.118033989t + t2 = 0.0000000001 Factor a perfect square on the left side: (t + -0.5590169945)(t + -0.5590169945) = 0.0000000001 Calculate the square root of the right side: 0.00001 Break this problem into two subproblems by setting (t + -0.5590169945) equal to 0.00001 and -0.00001.Subproblem 1
t + -0.5590169945 = 0.00001 Simplifying t + -0.5590169945 = 0.00001 Reorder the terms: -0.5590169945 + t = 0.00001 Solving -0.5590169945 + t = 0.00001 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5590169945' to each side of the equation. -0.5590169945 + 0.5590169945 + t = 0.00001 + 0.5590169945 Combine like terms: -0.5590169945 + 0.5590169945 = 0.0000000000 0.0000000000 + t = 0.00001 + 0.5590169945 t = 0.00001 + 0.5590169945 Combine like terms: 0.00001 + 0.5590169945 = 0.5590269945 t = 0.5590269945 Simplifying t = 0.5590269945Subproblem 2
t + -0.5590169945 = -0.00001 Simplifying t + -0.5590169945 = -0.00001 Reorder the terms: -0.5590169945 + t = -0.00001 Solving -0.5590169945 + t = -0.00001 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5590169945' to each side of the equation. -0.5590169945 + 0.5590169945 + t = -0.00001 + 0.5590169945 Combine like terms: -0.5590169945 + 0.5590169945 = 0.0000000000 0.0000000000 + t = -0.00001 + 0.5590169945 t = -0.00001 + 0.5590169945 Combine like terms: -0.00001 + 0.5590169945 = 0.5590069945 t = 0.5590069945 Simplifying t = 0.5590069945Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.5590269945, 0.5590069945}
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