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Simplifying t4 + -22t2 + 40 = 0 Reorder the terms: 40 + -22t2 + t4 = 0 Solving 40 + -22t2 + t4 = 0 Solving for variable 't'. Factor a trinomial. (2 + -1t2)(20 + -1t2) = 0Subproblem 1
Set the factor '(2 + -1t2)' equal to zero and attempt to solve: Simplifying 2 + -1t2 = 0 Solving 2 + -1t2 = 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 + -1t2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t2 = 0 + -2 -1t2 = 0 + -2 Combine like terms: 0 + -2 = -2 -1t2 = -2 Divide each side by '-1'. t2 = 2 Simplifying t2 = 2 Take the square root of each side: t = {-1.414213562, 1.414213562}Subproblem 2
Set the factor '(20 + -1t2)' equal to zero and attempt to solve: Simplifying 20 + -1t2 = 0 Solving 20 + -1t2 = 0 Move all terms containing t to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + -1t2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -1t2 = 0 + -20 -1t2 = 0 + -20 Combine like terms: 0 + -20 = -20 -1t2 = -20 Divide each side by '-1'. t2 = 20 Simplifying t2 = 20 Take the square root of each side: t = {-4.472135955, 4.472135955}Solution
t = {-1.414213562, 1.414213562, -4.472135955, 4.472135955}
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