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Simplifying 0 = -16t2 + 12t + 200 Reorder the terms: 0 = 200 + 12t + -16t2 Solving 0 = 200 + 12t + -16t2 Solving for variable 't'. Combine like terms: 0 + -200 = -200 -200 + -12t + 16t2 = 200 + 12t + -16t2 + -200 + -12t + 16t2 Reorder the terms: -200 + -12t + 16t2 = 200 + -200 + 12t + -12t + -16t2 + 16t2 Combine like terms: 200 + -200 = 0 -200 + -12t + 16t2 = 0 + 12t + -12t + -16t2 + 16t2 -200 + -12t + 16t2 = 12t + -12t + -16t2 + 16t2 Combine like terms: 12t + -12t = 0 -200 + -12t + 16t2 = 0 + -16t2 + 16t2 -200 + -12t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -200 + -12t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-50 + -3t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-50 + -3t + 4t2)' equal to zero and attempt to solve: Simplifying -50 + -3t + 4t2 = 0 Solving -50 + -3t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -12.5 + -0.75t + t2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -0.75t + 12.5 + t2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -0.75t + t2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -0.75t + t2 = 0 + 12.5 -0.75t + t2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -0.75t + t2 = 12.5 The t term is -0.75t. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75t + 0.140625 + t2 = 12.5 + 0.140625 Reorder the terms: 0.140625 + -0.75t + t2 = 12.5 + 0.140625 Combine like terms: 12.5 + 0.140625 = 12.640625 0.140625 + -0.75t + t2 = 12.640625 Factor a perfect square on the left side: (t + -0.375)(t + -0.375) = 12.640625 Calculate the square root of the right side: 3.555365663 Break this problem into two subproblems by setting (t + -0.375) equal to 3.555365663 and -3.555365663.Subproblem 1
t + -0.375 = 3.555365663 Simplifying t + -0.375 = 3.555365663 Reorder the terms: -0.375 + t = 3.555365663 Solving -0.375 + t = 3.555365663 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + t = 3.555365663 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + t = 3.555365663 + 0.375 t = 3.555365663 + 0.375 Combine like terms: 3.555365663 + 0.375 = 3.930365663 t = 3.930365663 Simplifying t = 3.930365663Subproblem 2
t + -0.375 = -3.555365663 Simplifying t + -0.375 = -3.555365663 Reorder the terms: -0.375 + t = -3.555365663 Solving -0.375 + t = -3.555365663 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + t = -3.555365663 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + t = -3.555365663 + 0.375 t = -3.555365663 + 0.375 Combine like terms: -3.555365663 + 0.375 = -3.180365663 t = -3.180365663 Simplifying t = -3.180365663Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.930365663, -3.180365663}Solution
t = {3.930365663, -3.180365663}
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