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Simplifying -16t2 + 5184 = t Reorder the terms: 5184 + -16t2 = t Solving 5184 + -16t2 = t Solving for variable 't'. Reorder the terms: 5184 + -1t + -16t2 = t + -1t Combine like terms: t + -1t = 0 5184 + -1t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -324 + 0.0625t + t2 = 0 Move the constant term to the right: Add '324' to each side of the equation. -324 + 0.0625t + 324 + t2 = 0 + 324 Reorder the terms: -324 + 324 + 0.0625t + t2 = 0 + 324 Combine like terms: -324 + 324 = 0 0 + 0.0625t + t2 = 0 + 324 0.0625t + t2 = 0 + 324 Combine like terms: 0 + 324 = 324 0.0625t + t2 = 324 The t term is 0.0625t. Take half its coefficient (0.03125). Square it (0.0009765625) and add it to both sides. Add '0.0009765625' to each side of the equation. 0.0625t + 0.0009765625 + t2 = 324 + 0.0009765625 Reorder the terms: 0.0009765625 + 0.0625t + t2 = 324 + 0.0009765625 Combine like terms: 324 + 0.0009765625 = 324.0009765625 0.0009765625 + 0.0625t + t2 = 324.0009765625 Factor a perfect square on the left side: (t + 0.03125)(t + 0.03125) = 324.0009765625 Calculate the square root of the right side: 18.000027127 Break this problem into two subproblems by setting (t + 0.03125) equal to 18.000027127 and -18.000027127.Subproblem 1
t + 0.03125 = 18.000027127 Simplifying t + 0.03125 = 18.000027127 Reorder the terms: 0.03125 + t = 18.000027127 Solving 0.03125 + t = 18.000027127 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.03125' to each side of the equation. 0.03125 + -0.03125 + t = 18.000027127 + -0.03125 Combine like terms: 0.03125 + -0.03125 = 0.00000 0.00000 + t = 18.000027127 + -0.03125 t = 18.000027127 + -0.03125 Combine like terms: 18.000027127 + -0.03125 = 17.968777127 t = 17.968777127 Simplifying t = 17.968777127Subproblem 2
t + 0.03125 = -18.000027127 Simplifying t + 0.03125 = -18.000027127 Reorder the terms: 0.03125 + t = -18.000027127 Solving 0.03125 + t = -18.000027127 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.03125' to each side of the equation. 0.03125 + -0.03125 + t = -18.000027127 + -0.03125 Combine like terms: 0.03125 + -0.03125 = 0.00000 0.00000 + t = -18.000027127 + -0.03125 t = -18.000027127 + -0.03125 Combine like terms: -18.000027127 + -0.03125 = -18.031277127 t = -18.031277127 Simplifying t = -18.031277127Solution
The solution to the problem is based on the solutions from the subproblems. t = {17.968777127, -18.031277127}
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