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Simplifying t4 + -5t2 + 6 = 0 Reorder the terms: 6 + -5t2 + t4 = 0 Solving 6 + -5t2 + t4 = 0 Solving for variable 't'. Factor a trinomial. (2 + -1t2)(3 + -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 '(3 + -1t2)' equal to zero and attempt to solve: Simplifying 3 + -1t2 = 0 Solving 3 + -1t2 = 0 Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1t2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1t2 = 0 + -3 -1t2 = 0 + -3 Combine like terms: 0 + -3 = -3 -1t2 = -3 Divide each side by '-1'. t2 = 3 Simplifying t2 = 3 Take the square root of each side: t = {-1.732050808, 1.732050808}Solution
t = {-1.414213562, 1.414213562, -1.732050808, 1.732050808}
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