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Simplifying 2t3 + -8t2 + -2t = 0 Reorder the terms: -2t + -8t2 + 2t3 = 0 Solving -2t + -8t2 + 2t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2t'. 2t(-1 + -4t + t2) = 0 Ignore the factor 2.Subproblem 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 '(-1 + -4t + t2)' equal to zero and attempt to solve: Simplifying -1 + -4t + t2 = 0 Solving -1 + -4t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -4t + 1 + t2 = 0 + 1 Reorder the terms: -1 + 1 + -4t + t2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4t + t2 = 0 + 1 -4t + t2 = 0 + 1 Combine like terms: 0 + 1 = 1 -4t + t2 = 1 The t term is -4t. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4t + 4 + t2 = 1 + 4 Reorder the terms: 4 + -4t + t2 = 1 + 4 Combine like terms: 1 + 4 = 5 4 + -4t + t2 = 5 Factor a perfect square on the left side: (t + -2)(t + -2) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (t + -2) equal to 2.236067978 and -2.236067978.Subproblem 1
t + -2 = 2.236067978 Simplifying t + -2 = 2.236067978 Reorder the terms: -2 + t = 2.236067978 Solving -2 + t = 2.236067978 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 2.236067978 + 2 Combine like terms: -2 + 2 = 0 0 + t = 2.236067978 + 2 t = 2.236067978 + 2 Combine like terms: 2.236067978 + 2 = 4.236067978 t = 4.236067978 Simplifying t = 4.236067978Subproblem 2
t + -2 = -2.236067978 Simplifying t + -2 = -2.236067978 Reorder the terms: -2 + t = -2.236067978 Solving -2 + t = -2.236067978 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -2.236067978 + 2 Combine like terms: -2 + 2 = 0 0 + t = -2.236067978 + 2 t = -2.236067978 + 2 Combine like terms: -2.236067978 + 2 = -0.236067978 t = -0.236067978 Simplifying t = -0.236067978Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.236067978, -0.236067978}Solution
t = {0, 4.236067978, -0.236067978}
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