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Simplifying t3 + -3t2 + -9t = 0 Reorder the terms: -9t + -3t2 + t3 = 0 Solving -9t + -3t2 + t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(-9 + -3t + t2) = 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 '(-9 + -3t + t2)' equal to zero and attempt to solve: Simplifying -9 + -3t + t2 = 0 Solving -9 + -3t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -3t + 9 + t2 = 0 + 9 Reorder the terms: -9 + 9 + -3t + t2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -3t + t2 = 0 + 9 -3t + t2 = 0 + 9 Combine like terms: 0 + 9 = 9 -3t + t2 = 9 The t term is -3t. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3t + 2.25 + t2 = 9 + 2.25 Reorder the terms: 2.25 + -3t + t2 = 9 + 2.25 Combine like terms: 9 + 2.25 = 11.25 2.25 + -3t + t2 = 11.25 Factor a perfect square on the left side: (t + -1.5)(t + -1.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (t + -1.5) equal to 3.354101966 and -3.354101966.Subproblem 1
t + -1.5 = 3.354101966 Simplifying t + -1.5 = 3.354101966 Reorder the terms: -1.5 + t = 3.354101966 Solving -1.5 + t = 3.354101966 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + t = 3.354101966 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = 3.354101966 + 1.5 t = 3.354101966 + 1.5 Combine like terms: 3.354101966 + 1.5 = 4.854101966 t = 4.854101966 Simplifying t = 4.854101966Subproblem 2
t + -1.5 = -3.354101966 Simplifying t + -1.5 = -3.354101966 Reorder the terms: -1.5 + t = -3.354101966 Solving -1.5 + t = -3.354101966 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + t = -3.354101966 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = -3.354101966 + 1.5 t = -3.354101966 + 1.5 Combine like terms: -3.354101966 + 1.5 = -1.854101966 t = -1.854101966 Simplifying t = -1.854101966Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.854101966, -1.854101966}Solution
t = {0, 4.854101966, -1.854101966}
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