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Simplifying 0 = -16t2 + 300t + 1.5 Reorder the terms: 0 = 1.5 + 300t + -16t2 Solving 0 = 1.5 + 300t + -16t2 Solving for variable 't'. Combine like terms: 0 + -1.5 = -1.5 -1.5 + -300t + 16t2 = 1.5 + 300t + -16t2 + -1.5 + -300t + 16t2 Reorder the terms: -1.5 + -300t + 16t2 = 1.5 + -1.5 + 300t + -300t + -16t2 + 16t2 Combine like terms: 1.5 + -1.5 = 0.0 -1.5 + -300t + 16t2 = 0.0 + 300t + -300t + -16t2 + 16t2 -1.5 + -300t + 16t2 = 300t + -300t + -16t2 + 16t2 Combine like terms: 300t + -300t = 0 -1.5 + -300t + 16t2 = 0 + -16t2 + 16t2 -1.5 + -300t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -1.5 + -300t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.09375 + -18.75t + t2 = 0 Move the constant term to the right: Add '0.09375' to each side of the equation. -0.09375 + -18.75t + 0.09375 + t2 = 0 + 0.09375 Reorder the terms: -0.09375 + 0.09375 + -18.75t + t2 = 0 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + -18.75t + t2 = 0 + 0.09375 -18.75t + t2 = 0 + 0.09375 Combine like terms: 0 + 0.09375 = 0.09375 -18.75t + t2 = 0.09375 The t term is -18.75t. Take half its coefficient (-9.375). Square it (87.890625) and add it to both sides. Add '87.890625' to each side of the equation. -18.75t + 87.890625 + t2 = 0.09375 + 87.890625 Reorder the terms: 87.890625 + -18.75t + t2 = 0.09375 + 87.890625 Combine like terms: 0.09375 + 87.890625 = 87.984375 87.890625 + -18.75t + t2 = 87.984375 Factor a perfect square on the left side: (t + -9.375)(t + -9.375) = 87.984375 Calculate the square root of the right side: 9.379998667 Break this problem into two subproblems by setting (t + -9.375) equal to 9.379998667 and -9.379998667.Subproblem 1
t + -9.375 = 9.379998667 Simplifying t + -9.375 = 9.379998667 Reorder the terms: -9.375 + t = 9.379998667 Solving -9.375 + t = 9.379998667 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9.375' to each side of the equation. -9.375 + 9.375 + t = 9.379998667 + 9.375 Combine like terms: -9.375 + 9.375 = 0.000 0.000 + t = 9.379998667 + 9.375 t = 9.379998667 + 9.375 Combine like terms: 9.379998667 + 9.375 = 18.754998667 t = 18.754998667 Simplifying t = 18.754998667Subproblem 2
t + -9.375 = -9.379998667 Simplifying t + -9.375 = -9.379998667 Reorder the terms: -9.375 + t = -9.379998667 Solving -9.375 + t = -9.379998667 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9.375' to each side of the equation. -9.375 + 9.375 + t = -9.379998667 + 9.375 Combine like terms: -9.375 + 9.375 = 0.000 0.000 + t = -9.379998667 + 9.375 t = -9.379998667 + 9.375 Combine like terms: -9.379998667 + 9.375 = -0.004998667 t = -0.004998667 Simplifying t = -0.004998667Solution
The solution to the problem is based on the solutions from the subproblems. t = {18.754998667, -0.004998667}
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