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Simplifying 0 = -16t2 + 3t + 15 Reorder the terms: 0 = 15 + 3t + -16t2 Solving 0 = 15 + 3t + -16t2 Solving for variable 't'. Combine like terms: 0 + -15 = -15 -15 + -3t + 16t2 = 15 + 3t + -16t2 + -15 + -3t + 16t2 Reorder the terms: -15 + -3t + 16t2 = 15 + -15 + 3t + -3t + -16t2 + 16t2 Combine like terms: 15 + -15 = 0 -15 + -3t + 16t2 = 0 + 3t + -3t + -16t2 + 16t2 -15 + -3t + 16t2 = 3t + -3t + -16t2 + 16t2 Combine like terms: 3t + -3t = 0 -15 + -3t + 16t2 = 0 + -16t2 + 16t2 -15 + -3t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -15 + -3t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.9375 + -0.1875t + t2 = 0 Move the constant term to the right: Add '0.9375' to each side of the equation. -0.9375 + -0.1875t + 0.9375 + t2 = 0 + 0.9375 Reorder the terms: -0.9375 + 0.9375 + -0.1875t + t2 = 0 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + -0.1875t + t2 = 0 + 0.9375 -0.1875t + t2 = 0 + 0.9375 Combine like terms: 0 + 0.9375 = 0.9375 -0.1875t + t2 = 0.9375 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 = 0.9375 + 0.0087890625 Reorder the terms: 0.0087890625 + -0.1875t + t2 = 0.9375 + 0.0087890625 Combine like terms: 0.9375 + 0.0087890625 = 0.9462890625 0.0087890625 + -0.1875t + t2 = 0.9462890625 Factor a perfect square on the left side: (t + -0.09375)(t + -0.09375) = 0.9462890625 Calculate the square root of the right side: 0.972773901 Break this problem into two subproblems by setting (t + -0.09375) equal to 0.972773901 and -0.972773901.Subproblem 1
t + -0.09375 = 0.972773901 Simplifying t + -0.09375 = 0.972773901 Reorder the terms: -0.09375 + t = 0.972773901 Solving -0.09375 + t = 0.972773901 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 = 0.972773901 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + t = 0.972773901 + 0.09375 t = 0.972773901 + 0.09375 Combine like terms: 0.972773901 + 0.09375 = 1.066523901 t = 1.066523901 Simplifying t = 1.066523901Subproblem 2
t + -0.09375 = -0.972773901 Simplifying t + -0.09375 = -0.972773901 Reorder the terms: -0.09375 + t = -0.972773901 Solving -0.09375 + t = -0.972773901 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 = -0.972773901 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + t = -0.972773901 + 0.09375 t = -0.972773901 + 0.09375 Combine like terms: -0.972773901 + 0.09375 = -0.879023901 t = -0.879023901 Simplifying t = -0.879023901Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.066523901, -0.879023901}
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