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Simplifying 60 = 50 + (2t + -0.0625t2) Remove parenthesis around (2t + -0.0625t2) 60 = 50 + 2t + -0.0625t2 Solving 60 = 50 + 2t + -0.0625t2 Solving for variable 't'. Combine like terms: 60 + -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 = 96 256 + -32t + t2 = 96 Factor a perfect square on the left side: (t + -16)(t + -16) = 96 Calculate the square root of the right side: 9.797958971 Break this problem into two subproblems by setting (t + -16) equal to 9.797958971 and -9.797958971.Subproblem 1
t + -16 = 9.797958971 Simplifying t + -16 = 9.797958971 Reorder the terms: -16 + t = 9.797958971 Solving -16 + t = 9.797958971 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 = 9.797958971 + 16 Combine like terms: -16 + 16 = 0 0 + t = 9.797958971 + 16 t = 9.797958971 + 16 Combine like terms: 9.797958971 + 16 = 25.797958971 t = 25.797958971 Simplifying t = 25.797958971Subproblem 2
t + -16 = -9.797958971 Simplifying t + -16 = -9.797958971 Reorder the terms: -16 + t = -9.797958971 Solving -16 + t = -9.797958971 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 = -9.797958971 + 16 Combine like terms: -16 + 16 = 0 0 + t = -9.797958971 + 16 t = -9.797958971 + 16 Combine like terms: -9.797958971 + 16 = 6.202041029 t = 6.202041029 Simplifying t = 6.202041029Solution
The solution to the problem is based on the solutions from the subproblems. t = {25.797958971, 6.202041029}
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