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Simplifying 6t2 + -48t + 21 = 0 Reorder the terms: 21 + -48t + 6t2 = 0 Solving 21 + -48t + 6t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '3'. 3(7 + -16t + 2t2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(7 + -16t + 2t2)' equal to zero and attempt to solve: Simplifying 7 + -16t + 2t2 = 0 Solving 7 + -16t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3.5 + -8t + t2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -8t + -3.5 + t2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -8t + t2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -8t + t2 = 0 + -3.5 -8t + t2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -8t + t2 = -3.5 The t term is -8t. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8t + 16 + t2 = -3.5 + 16 Reorder the terms: 16 + -8t + t2 = -3.5 + 16 Combine like terms: -3.5 + 16 = 12.5 16 + -8t + t2 = 12.5 Factor a perfect square on the left side: (t + -4)(t + -4) = 12.5 Calculate the square root of the right side: 3.535533906 Break this problem into two subproblems by setting (t + -4) equal to 3.535533906 and -3.535533906.Subproblem 1
t + -4 = 3.535533906 Simplifying t + -4 = 3.535533906 Reorder the terms: -4 + t = 3.535533906 Solving -4 + t = 3.535533906 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = 3.535533906 + 4 Combine like terms: -4 + 4 = 0 0 + t = 3.535533906 + 4 t = 3.535533906 + 4 Combine like terms: 3.535533906 + 4 = 7.535533906 t = 7.535533906 Simplifying t = 7.535533906Subproblem 2
t + -4 = -3.535533906 Simplifying t + -4 = -3.535533906 Reorder the terms: -4 + t = -3.535533906 Solving -4 + t = -3.535533906 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = -3.535533906 + 4 Combine like terms: -4 + 4 = 0 0 + t = -3.535533906 + 4 t = -3.535533906 + 4 Combine like terms: -3.535533906 + 4 = 0.464466094 t = 0.464466094 Simplifying t = 0.464466094Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.535533906, 0.464466094}Solution
t = {7.535533906, 0.464466094}
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