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Simplifying t2(t2 + -6) = -9 Reorder the terms: t2(-6 + t2) = -9 (-6 * t2 + t2 * t2) = -9 (-6t2 + t4) = -9 Solving -6t2 + t4 = -9 Solving for variable 't'. Reorder the terms: 9 + -6t2 + t4 = -9 + 9 Combine like terms: -9 + 9 = 0 9 + -6t2 + t4 = 0 Factor a trinomial. (3 + -1t2)(3 + -1t2) = 0Subproblem 1
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}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 = {-1.732050808, 1.732050808, -1.732050808, 1.732050808}
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