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