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Simplifying 0 = -16t2 + 3t + 8 Reorder the terms: 0 = 8 + 3t + -16t2 Solving 0 = 8 + 3t + -16t2 Solving for variable 't'. Combine like terms: 0 + -8 = -8 -8 + -3t + 16t2 = 8 + 3t + -16t2 + -8 + -3t + 16t2 Reorder the terms: -8 + -3t + 16t2 = 8 + -8 + 3t + -3t + -16t2 + 16t2 Combine like terms: 8 + -8 = 0 -8 + -3t + 16t2 = 0 + 3t + -3t + -16t2 + 16t2 -8 + -3t + 16t2 = 3t + -3t + -16t2 + 16t2 Combine like terms: 3t + -3t = 0 -8 + -3t + 16t2 = 0 + -16t2 + 16t2 -8 + -3t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -8 + -3t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.5 + -0.1875t + t2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -0.1875t + 0.5 + t2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -0.1875t + t2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -0.1875t + t2 = 0 + 0.5 -0.1875t + t2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -0.1875t + t2 = 0.5 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 = 0.5 + 0.0087890625 Reorder the terms: 0.0087890625 + -0.1875t + t2 = 0.5 + 0.0087890625 Combine like terms: 0.5 + 0.0087890625 = 0.5087890625 0.0087890625 + -0.1875t + t2 = 0.5087890625 Factor a perfect square on the left side: (t + -0.09375)(t + -0.09375) = 0.5087890625 Calculate the square root of the right side: 0.713294513 Break this problem into two subproblems by setting (t + -0.09375) equal to 0.713294513 and -0.713294513.Subproblem 1
t + -0.09375 = 0.713294513 Simplifying t + -0.09375 = 0.713294513 Reorder the terms: -0.09375 + t = 0.713294513 Solving -0.09375 + t = 0.713294513 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 = 0.713294513 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + t = 0.713294513 + 0.09375 t = 0.713294513 + 0.09375 Combine like terms: 0.713294513 + 0.09375 = 0.807044513 t = 0.807044513 Simplifying t = 0.807044513Subproblem 2
t + -0.09375 = -0.713294513 Simplifying t + -0.09375 = -0.713294513 Reorder the terms: -0.09375 + t = -0.713294513 Solving -0.09375 + t = -0.713294513 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 = -0.713294513 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + t = -0.713294513 + 0.09375 t = -0.713294513 + 0.09375 Combine like terms: -0.713294513 + 0.09375 = -0.619544513 t = -0.619544513 Simplifying t = -0.619544513Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.807044513, -0.619544513}
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