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Simplifying t = -16t2 + -30t + 200 Reorder the terms: t = 200 + -30t + -16t2 Solving t = 200 + -30t + -16t2 Solving for variable 't'. Reorder the terms: -200 + t + 30t + 16t2 = 200 + -30t + -16t2 + -200 + 30t + 16t2 Combine like terms: t + 30t = 31t -200 + 31t + 16t2 = 200 + -30t + -16t2 + -200 + 30t + 16t2 Reorder the terms: -200 + 31t + 16t2 = 200 + -200 + -30t + 30t + -16t2 + 16t2 Combine like terms: 200 + -200 = 0 -200 + 31t + 16t2 = 0 + -30t + 30t + -16t2 + 16t2 -200 + 31t + 16t2 = -30t + 30t + -16t2 + 16t2 Combine like terms: -30t + 30t = 0 -200 + 31t + 16t2 = 0 + -16t2 + 16t2 -200 + 31t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -200 + 31t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -12.5 + 1.9375t + t2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + 1.9375t + 12.5 + t2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + 1.9375t + t2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + 1.9375t + t2 = 0 + 12.5 1.9375t + t2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 1.9375t + t2 = 12.5 The t term is 1.9375t. Take half its coefficient (0.96875). Square it (0.9384765625) and add it to both sides. Add '0.9384765625' to each side of the equation. 1.9375t + 0.9384765625 + t2 = 12.5 + 0.9384765625 Reorder the terms: 0.9384765625 + 1.9375t + t2 = 12.5 + 0.9384765625 Combine like terms: 12.5 + 0.9384765625 = 13.4384765625 0.9384765625 + 1.9375t + t2 = 13.4384765625 Factor a perfect square on the left side: (t + 0.96875)(t + 0.96875) = 13.4384765625 Calculate the square root of the right side: 3.665852774 Break this problem into two subproblems by setting (t + 0.96875) equal to 3.665852774 and -3.665852774.Subproblem 1
t + 0.96875 = 3.665852774 Simplifying t + 0.96875 = 3.665852774 Reorder the terms: 0.96875 + t = 3.665852774 Solving 0.96875 + t = 3.665852774 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.96875' to each side of the equation. 0.96875 + -0.96875 + t = 3.665852774 + -0.96875 Combine like terms: 0.96875 + -0.96875 = 0.00000 0.00000 + t = 3.665852774 + -0.96875 t = 3.665852774 + -0.96875 Combine like terms: 3.665852774 + -0.96875 = 2.697102774 t = 2.697102774 Simplifying t = 2.697102774Subproblem 2
t + 0.96875 = -3.665852774 Simplifying t + 0.96875 = -3.665852774 Reorder the terms: 0.96875 + t = -3.665852774 Solving 0.96875 + t = -3.665852774 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.96875' to each side of the equation. 0.96875 + -0.96875 + t = -3.665852774 + -0.96875 Combine like terms: 0.96875 + -0.96875 = 0.00000 0.00000 + t = -3.665852774 + -0.96875 t = -3.665852774 + -0.96875 Combine like terms: -3.665852774 + -0.96875 = -4.634602774 t = -4.634602774 Simplifying t = -4.634602774Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.697102774, -4.634602774}
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