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Simplifying 0 = 16t2 + -300t + 1000 Reorder the terms: 0 = 1000 + -300t + 16t2 Solving 0 = 1000 + -300t + 16t2 Solving for variable 't'. Combine like terms: 0 + -1000 = -1000 -1000 + 300t + -16t2 = 1000 + -300t + 16t2 + -1000 + 300t + -16t2 Reorder the terms: -1000 + 300t + -16t2 = 1000 + -1000 + -300t + 300t + 16t2 + -16t2 Combine like terms: 1000 + -1000 = 0 -1000 + 300t + -16t2 = 0 + -300t + 300t + 16t2 + -16t2 -1000 + 300t + -16t2 = -300t + 300t + 16t2 + -16t2 Combine like terms: -300t + 300t = 0 -1000 + 300t + -16t2 = 0 + 16t2 + -16t2 -1000 + 300t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -1000 + 300t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-250 + 75t + -4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-250 + 75t + -4t2)' equal to zero and attempt to solve: Simplifying -250 + 75t + -4t2 = 0 Solving -250 + 75t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 62.5 + -18.75t + t2 = 0 Move the constant term to the right: Add '-62.5' to each side of the equation. 62.5 + -18.75t + -62.5 + t2 = 0 + -62.5 Reorder the terms: 62.5 + -62.5 + -18.75t + t2 = 0 + -62.5 Combine like terms: 62.5 + -62.5 = 0.0 0.0 + -18.75t + t2 = 0 + -62.5 -18.75t + t2 = 0 + -62.5 Combine like terms: 0 + -62.5 = -62.5 -18.75t + t2 = -62.5 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 = -62.5 + 87.890625 Reorder the terms: 87.890625 + -18.75t + t2 = -62.5 + 87.890625 Combine like terms: -62.5 + 87.890625 = 25.390625 87.890625 + -18.75t + t2 = 25.390625 Factor a perfect square on the left side: (t + -9.375)(t + -9.375) = 25.390625 Calculate the square root of the right side: 5.038911093 Break this problem into two subproblems by setting (t + -9.375) equal to 5.038911093 and -5.038911093.Subproblem 1
t + -9.375 = 5.038911093 Simplifying t + -9.375 = 5.038911093 Reorder the terms: -9.375 + t = 5.038911093 Solving -9.375 + t = 5.038911093 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 = 5.038911093 + 9.375 Combine like terms: -9.375 + 9.375 = 0.000 0.000 + t = 5.038911093 + 9.375 t = 5.038911093 + 9.375 Combine like terms: 5.038911093 + 9.375 = 14.413911093 t = 14.413911093 Simplifying t = 14.413911093Subproblem 2
t + -9.375 = -5.038911093 Simplifying t + -9.375 = -5.038911093 Reorder the terms: -9.375 + t = -5.038911093 Solving -9.375 + t = -5.038911093 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 = -5.038911093 + 9.375 Combine like terms: -9.375 + 9.375 = 0.000 0.000 + t = -5.038911093 + 9.375 t = -5.038911093 + 9.375 Combine like terms: -5.038911093 + 9.375 = 4.336088907 t = 4.336088907 Simplifying t = 4.336088907Solution
The solution to the problem is based on the solutions from the subproblems. t = {14.413911093, 4.336088907}Solution
t = {14.413911093, 4.336088907}
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