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Simplifying 0 = -16t2 + 3t + 4 Reorder the terms: 0 = 4 + 3t + -16t2 Solving 0 = 4 + 3t + -16t2 Solving for variable 't'. Combine like terms: 0 + -4 = -4 -4 + -3t + 16t2 = 4 + 3t + -16t2 + -4 + -3t + 16t2 Reorder the terms: -4 + -3t + 16t2 = 4 + -4 + 3t + -3t + -16t2 + 16t2 Combine like terms: 4 + -4 = 0 -4 + -3t + 16t2 = 0 + 3t + -3t + -16t2 + 16t2 -4 + -3t + 16t2 = 3t + -3t + -16t2 + 16t2 Combine like terms: 3t + -3t = 0 -4 + -3t + 16t2 = 0 + -16t2 + 16t2 -4 + -3t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -4 + -3t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.25 + -0.1875t + t2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -0.1875t + 0.25 + t2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -0.1875t + t2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -0.1875t + t2 = 0 + 0.25 -0.1875t + t2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -0.1875t + t2 = 0.25 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 = 0.25 + 0.0087890625 Reorder the terms: 0.0087890625 + -0.1875t + t2 = 0.25 + 0.0087890625 Combine like terms: 0.25 + 0.0087890625 = 0.2587890625 0.0087890625 + -0.1875t + t2 = 0.2587890625 Factor a perfect square on the left side: (t + -0.09375)(t + -0.09375) = 0.2587890625 Calculate the square root of the right side: 0.508713144 Break this problem into two subproblems by setting (t + -0.09375) equal to 0.508713144 and -0.508713144.Subproblem 1
t + -0.09375 = 0.508713144 Simplifying t + -0.09375 = 0.508713144 Reorder the terms: -0.09375 + t = 0.508713144 Solving -0.09375 + t = 0.508713144 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 = 0.508713144 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + t = 0.508713144 + 0.09375 t = 0.508713144 + 0.09375 Combine like terms: 0.508713144 + 0.09375 = 0.602463144 t = 0.602463144 Simplifying t = 0.602463144Subproblem 2
t + -0.09375 = -0.508713144 Simplifying t + -0.09375 = -0.508713144 Reorder the terms: -0.09375 + t = -0.508713144 Solving -0.09375 + t = -0.508713144 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 = -0.508713144 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + t = -0.508713144 + 0.09375 t = -0.508713144 + 0.09375 Combine like terms: -0.508713144 + 0.09375 = -0.414963144 t = -0.414963144 Simplifying t = -0.414963144Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.602463144, -0.414963144}
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