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Simplifying 4t4 + -5t2 = -1 Reorder the terms: -5t2 + 4t4 = -1 Solving -5t2 + 4t4 = -1 Solving for variable 't'. Reorder the terms: 1 + -5t2 + 4t4 = -1 + 1 Combine like terms: -1 + 1 = 0 1 + -5t2 + 4t4 = 0 Factor a trinomial. (1 + -4t2)(1 + -1t2) = 0 Factor a difference between two squares. ((1 + 2t)(1 + -2t))(1 + -1t2) = 0 Factor a difference between two squares. ((1 + t)(1 + -1t))(1 + 2t)(1 + -2t) = 0Subproblem 1
Set the factor '(1 + 2t)' equal to zero and attempt to solve: Simplifying 1 + 2t = 0 Solving 1 + 2t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2t = 0 + -1 2t = 0 + -1 Combine like terms: 0 + -1 = -1 2t = -1 Divide each side by '2'. t = -0.5 Simplifying t = -0.5Subproblem 2
Set the factor '(1 + -2t)' equal to zero and attempt to solve: Simplifying 1 + -2t = 0 Solving 1 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2t = 0 + -1 -2t = 0 + -1 Combine like terms: 0 + -1 = -1 -2t = -1 Divide each side by '-2'. t = 0.5 Simplifying t = 0.5Subproblem 3
Set the factor '(1 + t)' equal to zero and attempt to solve: Simplifying 1 + t = 0 Solving 1 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + t = 0 + -1 t = 0 + -1 Combine like terms: 0 + -1 = -1 t = -1 Simplifying t = -1Subproblem 4
Set the factor '(1 + -1t)' equal to zero and attempt to solve: Simplifying 1 + -1t = 0 Solving 1 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1t = 0 + -1 -1t = 0 + -1 Combine like terms: 0 + -1 = -1 -1t = -1 Divide each side by '-1'. t = 1 Simplifying t = 1Solution
t = {-0.5, 0.5, -1, 1}
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