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Simplifying -3t2 + -48t + 9 = 0 Reorder the terms: 9 + -48t + -3t2 = 0 Solving 9 + -48t + -3t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '3'. 3(3 + -16t + -1t2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + -16t + -1t2)' equal to zero and attempt to solve: Simplifying 3 + -16t + -1t2 = 0 Solving 3 + -16t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3 + 16t + t2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 16t + 3 + t2 = 0 + 3 Reorder the terms: -3 + 3 + 16t + t2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 16t + t2 = 0 + 3 16t + t2 = 0 + 3 Combine like terms: 0 + 3 = 3 16t + t2 = 3 The t term is 16t. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16t + 64 + t2 = 3 + 64 Reorder the terms: 64 + 16t + t2 = 3 + 64 Combine like terms: 3 + 64 = 67 64 + 16t + t2 = 67 Factor a perfect square on the left side: (t + 8)(t + 8) = 67 Calculate the square root of the right side: 8.185352772 Break this problem into two subproblems by setting (t + 8) equal to 8.185352772 and -8.185352772.Subproblem 1
t + 8 = 8.185352772 Simplifying t + 8 = 8.185352772 Reorder the terms: 8 + t = 8.185352772 Solving 8 + t = 8.185352772 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + t = 8.185352772 + -8 Combine like terms: 8 + -8 = 0 0 + t = 8.185352772 + -8 t = 8.185352772 + -8 Combine like terms: 8.185352772 + -8 = 0.185352772 t = 0.185352772 Simplifying t = 0.185352772Subproblem 2
t + 8 = -8.185352772 Simplifying t + 8 = -8.185352772 Reorder the terms: 8 + t = -8.185352772 Solving 8 + t = -8.185352772 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + t = -8.185352772 + -8 Combine like terms: 8 + -8 = 0 0 + t = -8.185352772 + -8 t = -8.185352772 + -8 Combine like terms: -8.185352772 + -8 = -16.185352772 t = -16.185352772 Simplifying t = -16.185352772Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.185352772, -16.185352772}Solution
t = {0.185352772, -16.185352772}
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