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Simplifying 0 = -0.0625t2 + 3t + -20 Reorder the terms: 0 = -20 + 3t + -0.0625t2 Solving 0 = -20 + 3t + -0.0625t2 Solving for variable 't'. Combine like terms: 0 + 20 = 20 20 + -3t + 0.0625t2 = -20 + 3t + -0.0625t2 + 20 + -3t + 0.0625t2 Reorder the terms: 20 + -3t + 0.0625t2 = -20 + 20 + 3t + -3t + -0.0625t2 + 0.0625t2 Combine like terms: -20 + 20 = 0 20 + -3t + 0.0625t2 = 0 + 3t + -3t + -0.0625t2 + 0.0625t2 20 + -3t + 0.0625t2 = 3t + -3t + -0.0625t2 + 0.0625t2 Combine like terms: 3t + -3t = 0 20 + -3t + 0.0625t2 = 0 + -0.0625t2 + 0.0625t2 20 + -3t + 0.0625t2 = -0.0625t2 + 0.0625t2 Combine like terms: -0.0625t2 + 0.0625t2 = 0.0000 20 + -3t + 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'. 320 + -48t + t2 = 0 Move the constant term to the right: Add '-320' to each side of the equation. 320 + -48t + -320 + t2 = 0 + -320 Reorder the terms: 320 + -320 + -48t + t2 = 0 + -320 Combine like terms: 320 + -320 = 0 0 + -48t + t2 = 0 + -320 -48t + t2 = 0 + -320 Combine like terms: 0 + -320 = -320 -48t + t2 = -320 The t term is -48t. Take half its coefficient (-24). Square it (576) and add it to both sides. Add '576' to each side of the equation. -48t + 576 + t2 = -320 + 576 Reorder the terms: 576 + -48t + t2 = -320 + 576 Combine like terms: -320 + 576 = 256 576 + -48t + t2 = 256 Factor a perfect square on the left side: (t + -24)(t + -24) = 256 Calculate the square root of the right side: 16 Break this problem into two subproblems by setting (t + -24) equal to 16 and -16.Subproblem 1
t + -24 = 16 Simplifying t + -24 = 16 Reorder the terms: -24 + t = 16 Solving -24 + t = 16 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + t = 16 + 24 Combine like terms: -24 + 24 = 0 0 + t = 16 + 24 t = 16 + 24 Combine like terms: 16 + 24 = 40 t = 40 Simplifying t = 40Subproblem 2
t + -24 = -16 Simplifying t + -24 = -16 Reorder the terms: -24 + t = -16 Solving -24 + t = -16 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + t = -16 + 24 Combine like terms: -24 + 24 = 0 0 + t = -16 + 24 t = -16 + 24 Combine like terms: -16 + 24 = 8 t = 8 Simplifying t = 8Solution
The solution to the problem is based on the solutions from the subproblems. t = {40, 8}
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