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Simplifying 2t3 + -9t2 + -12t = 0 Reorder the terms: -12t + -9t2 + 2t3 = 0 Solving -12t + -9t2 + 2t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(-12 + -9t + 2t2) = 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 '(-12 + -9t + 2t2)' equal to zero and attempt to solve: Simplifying -12 + -9t + 2t2 = 0 Solving -12 + -9t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6 + -4.5t + t2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -4.5t + 6 + t2 = 0 + 6 Reorder the terms: -6 + 6 + -4.5t + t2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -4.5t + t2 = 0 + 6 -4.5t + t2 = 0 + 6 Combine like terms: 0 + 6 = 6 -4.5t + t2 = 6 The t term is -4.5t. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5t + 5.0625 + t2 = 6 + 5.0625 Reorder the terms: 5.0625 + -4.5t + t2 = 6 + 5.0625 Combine like terms: 6 + 5.0625 = 11.0625 5.0625 + -4.5t + t2 = 11.0625 Factor a perfect square on the left side: (t + -2.25)(t + -2.25) = 11.0625 Calculate the square root of the right side: 3.326033674 Break this problem into two subproblems by setting (t + -2.25) equal to 3.326033674 and -3.326033674.Subproblem 1
t + -2.25 = 3.326033674 Simplifying t + -2.25 = 3.326033674 Reorder the terms: -2.25 + t = 3.326033674 Solving -2.25 + t = 3.326033674 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + t = 3.326033674 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + t = 3.326033674 + 2.25 t = 3.326033674 + 2.25 Combine like terms: 3.326033674 + 2.25 = 5.576033674 t = 5.576033674 Simplifying t = 5.576033674Subproblem 2
t + -2.25 = -3.326033674 Simplifying t + -2.25 = -3.326033674 Reorder the terms: -2.25 + t = -3.326033674 Solving -2.25 + t = -3.326033674 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + t = -3.326033674 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + t = -3.326033674 + 2.25 t = -3.326033674 + 2.25 Combine like terms: -3.326033674 + 2.25 = -1.076033674 t = -1.076033674 Simplifying t = -1.076033674Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.576033674, -1.076033674}Solution
t = {0, 5.576033674, -1.076033674}
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