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Simplifying 2t3 + -1t2 + -2t = 0 Reorder the terms: -2t + -1t2 + 2t3 = 0 Solving -2t + -1t2 + 2t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(-2 + -1t + 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 '(-2 + -1t + 2t2)' equal to zero and attempt to solve: Simplifying -2 + -1t + 2t2 = 0 Solving -2 + -1t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1 + -0.5t + t2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.5t + 1 + t2 = 0 + 1 Reorder the terms: -1 + 1 + -0.5t + t2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.5t + t2 = 0 + 1 -0.5t + t2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.5t + t2 = 1 The t term is -0.5t. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5t + 0.0625 + t2 = 1 + 0.0625 Reorder the terms: 0.0625 + -0.5t + t2 = 1 + 0.0625 Combine like terms: 1 + 0.0625 = 1.0625 0.0625 + -0.5t + t2 = 1.0625 Factor a perfect square on the left side: (t + -0.25)(t + -0.25) = 1.0625 Calculate the square root of the right side: 1.030776406 Break this problem into two subproblems by setting (t + -0.25) equal to 1.030776406 and -1.030776406.Subproblem 1
t + -0.25 = 1.030776406 Simplifying t + -0.25 = 1.030776406 Reorder the terms: -0.25 + t = 1.030776406 Solving -0.25 + t = 1.030776406 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + t = 1.030776406 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + t = 1.030776406 + 0.25 t = 1.030776406 + 0.25 Combine like terms: 1.030776406 + 0.25 = 1.280776406 t = 1.280776406 Simplifying t = 1.280776406Subproblem 2
t + -0.25 = -1.030776406 Simplifying t + -0.25 = -1.030776406 Reorder the terms: -0.25 + t = -1.030776406 Solving -0.25 + t = -1.030776406 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + t = -1.030776406 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + t = -1.030776406 + 0.25 t = -1.030776406 + 0.25 Combine like terms: -1.030776406 + 0.25 = -0.780776406 t = -0.780776406 Simplifying t = -0.780776406Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.280776406, -0.780776406}Solution
t = {0, 1.280776406, -0.780776406}
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