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Simplifying 3t3 + -38t2 + -28t = 0 Reorder the terms: -28t + -38t2 + 3t3 = 0 Solving -28t + -38t2 + 3t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(-28 + -38t + 3t2) = 0Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
Set the factor '(-28 + -38t + 3t2)' equal to zero and attempt to solve: Simplifying -28 + -38t + 3t2 = 0 Solving -28 + -38t + 3t2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -9.333333333 + -12.66666667t + t2 = 0 Move the constant term to the right: Add '9.333333333' to each side of the equation. -9.333333333 + -12.66666667t + 9.333333333 + t2 = 0 + 9.333333333 Reorder the terms: -9.333333333 + 9.333333333 + -12.66666667t + t2 = 0 + 9.333333333 Combine like terms: -9.333333333 + 9.333333333 = 0.000000000 0.000000000 + -12.66666667t + t2 = 0 + 9.333333333 -12.66666667t + t2 = 0 + 9.333333333 Combine like terms: 0 + 9.333333333 = 9.333333333 -12.66666667t + t2 = 9.333333333 The t term is -12.66666667t. Take half its coefficient (-6.333333335). Square it (40.11111113) and add it to both sides. Add '40.11111113' to each side of the equation. -12.66666667t + 40.11111113 + t2 = 9.333333333 + 40.11111113 Reorder the terms: 40.11111113 + -12.66666667t + t2 = 9.333333333 + 40.11111113 Combine like terms: 9.333333333 + 40.11111113 = 49.444444463 40.11111113 + -12.66666667t + t2 = 49.444444463 Factor a perfect square on the left side: (t + -6.333333335)(t + -6.333333335) = 49.444444463 Calculate the square root of the right side: 7.031674371 Break this problem into two subproblems by setting (t + -6.333333335) equal to 7.031674371 and -7.031674371.Subproblem 1
t + -6.333333335 = 7.031674371 Simplifying t + -6.333333335 = 7.031674371 Reorder the terms: -6.333333335 + t = 7.031674371 Solving -6.333333335 + t = 7.031674371 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.333333335' to each side of the equation. -6.333333335 + 6.333333335 + t = 7.031674371 + 6.333333335 Combine like terms: -6.333333335 + 6.333333335 = 0.000000000 0.000000000 + t = 7.031674371 + 6.333333335 t = 7.031674371 + 6.333333335 Combine like terms: 7.031674371 + 6.333333335 = 13.365007706 t = 13.365007706 Simplifying t = 13.365007706Subproblem 2
t + -6.333333335 = -7.031674371 Simplifying t + -6.333333335 = -7.031674371 Reorder the terms: -6.333333335 + t = -7.031674371 Solving -6.333333335 + t = -7.031674371 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.333333335' to each side of the equation. -6.333333335 + 6.333333335 + t = -7.031674371 + 6.333333335 Combine like terms: -6.333333335 + 6.333333335 = 0.000000000 0.000000000 + t = -7.031674371 + 6.333333335 t = -7.031674371 + 6.333333335 Combine like terms: -7.031674371 + 6.333333335 = -0.698341036 t = -0.698341036 Simplifying t = -0.698341036Solution
The solution to the problem is based on the solutions from the subproblems. t = {13.365007706, -0.698341036}Solution
t = {0, 13.365007706, -0.698341036}
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