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Simplifying 60(t) = 16 + -1t2 Solving 60t = 16 + -1t2 Solving for variable 't'. Reorder the terms: -16 + 60t + t2 = 16 + -1t2 + -16 + t2 Reorder the terms: -16 + 60t + t2 = 16 + -16 + -1t2 + t2 Combine like terms: 16 + -16 = 0 -16 + 60t + t2 = 0 + -1t2 + t2 -16 + 60t + t2 = -1t2 + t2 Combine like terms: -1t2 + t2 = 0 -16 + 60t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 60t + 16 + t2 = 0 + 16 Reorder the terms: -16 + 16 + 60t + t2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 60t + t2 = 0 + 16 60t + t2 = 0 + 16 Combine like terms: 0 + 16 = 16 60t + t2 = 16 The t term is 60t. Take half its coefficient (30). Square it (900) and add it to both sides. Add '900' to each side of the equation. 60t + 900 + t2 = 16 + 900 Reorder the terms: 900 + 60t + t2 = 16 + 900 Combine like terms: 16 + 900 = 916 900 + 60t + t2 = 916 Factor a perfect square on the left side: (t + 30)(t + 30) = 916 Calculate the square root of the right side: 30.265491901 Break this problem into two subproblems by setting (t + 30) equal to 30.265491901 and -30.265491901.Subproblem 1
t + 30 = 30.265491901 Simplifying t + 30 = 30.265491901 Reorder the terms: 30 + t = 30.265491901 Solving 30 + t = 30.265491901 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + t = 30.265491901 + -30 Combine like terms: 30 + -30 = 0 0 + t = 30.265491901 + -30 t = 30.265491901 + -30 Combine like terms: 30.265491901 + -30 = 0.265491901 t = 0.265491901 Simplifying t = 0.265491901Subproblem 2
t + 30 = -30.265491901 Simplifying t + 30 = -30.265491901 Reorder the terms: 30 + t = -30.265491901 Solving 30 + t = -30.265491901 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + t = -30.265491901 + -30 Combine like terms: 30 + -30 = 0 0 + t = -30.265491901 + -30 t = -30.265491901 + -30 Combine like terms: -30.265491901 + -30 = -60.265491901 t = -60.265491901 Simplifying t = -60.265491901Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.265491901, -60.265491901}
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