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Simplifying 3t = -16t2 + 50 Reorder the terms: 3t = 50 + -16t2 Solving 3t = 50 + -16t2 Solving for variable 't'. Reorder the terms: -50 + 3t + 16t2 = 50 + -16t2 + -50 + 16t2 Reorder the terms: -50 + 3t + 16t2 = 50 + -50 + -16t2 + 16t2 Combine like terms: 50 + -50 = 0 -50 + 3t + 16t2 = 0 + -16t2 + 16t2 -50 + 3t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -50 + 3t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -3.125 + 0.1875t + t2 = 0 Move the constant term to the right: Add '3.125' to each side of the equation. -3.125 + 0.1875t + 3.125 + t2 = 0 + 3.125 Reorder the terms: -3.125 + 3.125 + 0.1875t + t2 = 0 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + 0.1875t + t2 = 0 + 3.125 0.1875t + t2 = 0 + 3.125 Combine like terms: 0 + 3.125 = 3.125 0.1875t + t2 = 3.125 The t term is 0.1875t. Take half its coefficient (0.09375). Square it (0.0087890625) and add it to both sides. Add '0.0087890625' to each side of the equation. 0.1875t + 0.0087890625 + t2 = 3.125 + 0.0087890625 Reorder the terms: 0.0087890625 + 0.1875t + t2 = 3.125 + 0.0087890625 Combine like terms: 3.125 + 0.0087890625 = 3.1337890625 0.0087890625 + 0.1875t + t2 = 3.1337890625 Factor a perfect square on the left side: (t + 0.09375)(t + 0.09375) = 3.1337890625 Calculate the square root of the right side: 1.77025113 Break this problem into two subproblems by setting (t + 0.09375) equal to 1.77025113 and -1.77025113.Subproblem 1
t + 0.09375 = 1.77025113 Simplifying t + 0.09375 = 1.77025113 Reorder the terms: 0.09375 + t = 1.77025113 Solving 0.09375 + t = 1.77025113 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.09375' to each side of the equation. 0.09375 + -0.09375 + t = 1.77025113 + -0.09375 Combine like terms: 0.09375 + -0.09375 = 0.00000 0.00000 + t = 1.77025113 + -0.09375 t = 1.77025113 + -0.09375 Combine like terms: 1.77025113 + -0.09375 = 1.67650113 t = 1.67650113 Simplifying t = 1.67650113Subproblem 2
t + 0.09375 = -1.77025113 Simplifying t + 0.09375 = -1.77025113 Reorder the terms: 0.09375 + t = -1.77025113 Solving 0.09375 + t = -1.77025113 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.09375' to each side of the equation. 0.09375 + -0.09375 + t = -1.77025113 + -0.09375 Combine like terms: 0.09375 + -0.09375 = 0.00000 0.00000 + t = -1.77025113 + -0.09375 t = -1.77025113 + -0.09375 Combine like terms: -1.77025113 + -0.09375 = -1.86400113 t = -1.86400113 Simplifying t = -1.86400113Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.67650113, -1.86400113}
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