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Simplifying 40 = 50 + 2t + -0.0625t2 Solving 40 = 50 + 2t + -0.0625t2 Solving for variable 't'. Combine like terms: 40 + -50 = -10 -10 + -2t + 0.0625t2 = 50 + 2t + -0.0625t2 + -50 + -2t + 0.0625t2 Reorder the terms: -10 + -2t + 0.0625t2 = 50 + -50 + 2t + -2t + -0.0625t2 + 0.0625t2 Combine like terms: 50 + -50 = 0 -10 + -2t + 0.0625t2 = 0 + 2t + -2t + -0.0625t2 + 0.0625t2 -10 + -2t + 0.0625t2 = 2t + -2t + -0.0625t2 + 0.0625t2 Combine like terms: 2t + -2t = 0 -10 + -2t + 0.0625t2 = 0 + -0.0625t2 + 0.0625t2 -10 + -2t + 0.0625t2 = -0.0625t2 + 0.0625t2 Combine like terms: -0.0625t2 + 0.0625t2 = 0.0000 -10 + -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'. -160 + -32t + t2 = 0 Move the constant term to the right: Add '160' to each side of the equation. -160 + -32t + 160 + t2 = 0 + 160 Reorder the terms: -160 + 160 + -32t + t2 = 0 + 160 Combine like terms: -160 + 160 = 0 0 + -32t + t2 = 0 + 160 -32t + t2 = 0 + 160 Combine like terms: 0 + 160 = 160 -32t + t2 = 160 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 = 160 + 256 Reorder the terms: 256 + -32t + t2 = 160 + 256 Combine like terms: 160 + 256 = 416 256 + -32t + t2 = 416 Factor a perfect square on the left side: (t + -16)(t + -16) = 416 Calculate the square root of the right side: 20.396078054 Break this problem into two subproblems by setting (t + -16) equal to 20.396078054 and -20.396078054.Subproblem 1
t + -16 = 20.396078054 Simplifying t + -16 = 20.396078054 Reorder the terms: -16 + t = 20.396078054 Solving -16 + t = 20.396078054 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 = 20.396078054 + 16 Combine like terms: -16 + 16 = 0 0 + t = 20.396078054 + 16 t = 20.396078054 + 16 Combine like terms: 20.396078054 + 16 = 36.396078054 t = 36.396078054 Simplifying t = 36.396078054Subproblem 2
t + -16 = -20.396078054 Simplifying t + -16 = -20.396078054 Reorder the terms: -16 + t = -20.396078054 Solving -16 + t = -20.396078054 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 = -20.396078054 + 16 Combine like terms: -16 + 16 = 0 0 + t = -20.396078054 + 16 t = -20.396078054 + 16 Combine like terms: -20.396078054 + 16 = -4.396078054 t = -4.396078054 Simplifying t = -4.396078054Solution
The solution to the problem is based on the solutions from the subproblems. t = {36.396078054, -4.396078054}
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