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Simplifying 10 = 50 + 2t + -0.0625t2 Solving 10 = 50 + 2t + -0.0625t2 Solving for variable 't'. Combine like terms: 10 + -50 = -40 -40 + -2t + 0.0625t2 = 50 + 2t + -0.0625t2 + -50 + -2t + 0.0625t2 Reorder the terms: -40 + -2t + 0.0625t2 = 50 + -50 + 2t + -2t + -0.0625t2 + 0.0625t2 Combine like terms: 50 + -50 = 0 -40 + -2t + 0.0625t2 = 0 + 2t + -2t + -0.0625t2 + 0.0625t2 -40 + -2t + 0.0625t2 = 2t + -2t + -0.0625t2 + 0.0625t2 Combine like terms: 2t + -2t = 0 -40 + -2t + 0.0625t2 = 0 + -0.0625t2 + 0.0625t2 -40 + -2t + 0.0625t2 = -0.0625t2 + 0.0625t2 Combine like terms: -0.0625t2 + 0.0625t2 = 0.0000 -40 + -2t + 0.0625t2 = 0.0000 Begin completing the square. Divide all terms by 0.0625 the coefficient of the squared term: Divide each side by '0.0625'. -640 + -32t + t2 = 0 Move the constant term to the right: Add '640' to each side of the equation. -640 + -32t + 640 + t2 = 0 + 640 Reorder the terms: -640 + 640 + -32t + t2 = 0 + 640 Combine like terms: -640 + 640 = 0 0 + -32t + t2 = 0 + 640 -32t + t2 = 0 + 640 Combine like terms: 0 + 640 = 640 -32t + t2 = 640 The t term is -32t. Take half its coefficient (-16). Square it (256) and add it to both sides. Add '256' to each side of the equation. -32t + 256 + t2 = 640 + 256 Reorder the terms: 256 + -32t + t2 = 640 + 256 Combine like terms: 640 + 256 = 896 256 + -32t + t2 = 896 Factor a perfect square on the left side: (t + -16)(t + -16) = 896 Calculate the square root of the right side: 29.933259094 Break this problem into two subproblems by setting (t + -16) equal to 29.933259094 and -29.933259094.Subproblem 1
t + -16 = 29.933259094 Simplifying t + -16 = 29.933259094 Reorder the terms: -16 + t = 29.933259094 Solving -16 + t = 29.933259094 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + t = 29.933259094 + 16 Combine like terms: -16 + 16 = 0 0 + t = 29.933259094 + 16 t = 29.933259094 + 16 Combine like terms: 29.933259094 + 16 = 45.933259094 t = 45.933259094 Simplifying t = 45.933259094Subproblem 2
t + -16 = -29.933259094 Simplifying t + -16 = -29.933259094 Reorder the terms: -16 + t = -29.933259094 Solving -16 + t = -29.933259094 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + t = -29.933259094 + 16 Combine like terms: -16 + 16 = 0 0 + t = -29.933259094 + 16 t = -29.933259094 + 16 Combine like terms: -29.933259094 + 16 = -13.933259094 t = -13.933259094 Simplifying t = -13.933259094Solution
The solution to the problem is based on the solutions from the subproblems. t = {45.933259094, -13.933259094}
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