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Simplifying 1600 + -16t2 = t Solving 1600 + -16t2 = t Solving for variable 't'. Reorder the terms: 1600 + -1t + -16t2 = t + -1t Combine like terms: t + -1t = 0 1600 + -1t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -100 + 0.0625t + t2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + 0.0625t + 100 + t2 = 0 + 100 Reorder the terms: -100 + 100 + 0.0625t + t2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 0.0625t + t2 = 0 + 100 0.0625t + t2 = 0 + 100 Combine like terms: 0 + 100 = 100 0.0625t + t2 = 100 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 = 100 + 0.0009765625 Reorder the terms: 0.0009765625 + 0.0625t + t2 = 100 + 0.0009765625 Combine like terms: 100 + 0.0009765625 = 100.0009765625 0.0009765625 + 0.0625t + t2 = 100.0009765625 Factor a perfect square on the left side: (t + 0.03125)(t + 0.03125) = 100.0009765625 Calculate the square root of the right side: 10.000048828 Break this problem into two subproblems by setting (t + 0.03125) equal to 10.000048828 and -10.000048828.Subproblem 1
t + 0.03125 = 10.000048828 Simplifying t + 0.03125 = 10.000048828 Reorder the terms: 0.03125 + t = 10.000048828 Solving 0.03125 + t = 10.000048828 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 = 10.000048828 + -0.03125 Combine like terms: 0.03125 + -0.03125 = 0.00000 0.00000 + t = 10.000048828 + -0.03125 t = 10.000048828 + -0.03125 Combine like terms: 10.000048828 + -0.03125 = 9.968798828 t = 9.968798828 Simplifying t = 9.968798828Subproblem 2
t + 0.03125 = -10.000048828 Simplifying t + 0.03125 = -10.000048828 Reorder the terms: 0.03125 + t = -10.000048828 Solving 0.03125 + t = -10.000048828 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 = -10.000048828 + -0.03125 Combine like terms: 0.03125 + -0.03125 = 0.00000 0.00000 + t = -10.000048828 + -0.03125 t = -10.000048828 + -0.03125 Combine like terms: -10.000048828 + -0.03125 = -10.031298828 t = -10.031298828 Simplifying t = -10.031298828Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.968798828, -10.031298828}
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