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Simplifying g4 + -18g2 + 81 = 0 Reorder the terms: 81 + -18g2 + g4 = 0 Solving 81 + -18g2 + g4 = 0 Solving for variable 'g'. Factor a trinomial. (9 + -1g2)(9 + -1g2) = 0 Factor a difference between two squares. ((3 + g)(3 + -1g))(9 + -1g2) = 0 Factor a difference between two squares. ((3 + g)(3 + -1g))(3 + g)(3 + -1g) = 0Subproblem 1
Set the factor '(3 + g)' equal to zero and attempt to solve: Simplifying 3 + g = 0 Solving 3 + g = 0 Move all terms containing g to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + g = 0 + -3 Combine like terms: 3 + -3 = 0 0 + g = 0 + -3 g = 0 + -3 Combine like terms: 0 + -3 = -3 g = -3 Simplifying g = -3Subproblem 2
Set the factor '(3 + -1g)' equal to zero and attempt to solve: Simplifying 3 + -1g = 0 Solving 3 + -1g = 0 Move all terms containing g to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1g = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1g = 0 + -3 -1g = 0 + -3 Combine like terms: 0 + -3 = -3 -1g = -3 Divide each side by '-1'. g = 3 Simplifying g = 3Subproblem 3
Set the factor '(3 + g)' equal to zero and attempt to solve: Simplifying 3 + g = 0 Solving 3 + g = 0 Move all terms containing g to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + g = 0 + -3 Combine like terms: 3 + -3 = 0 0 + g = 0 + -3 g = 0 + -3 Combine like terms: 0 + -3 = -3 g = -3 Simplifying g = -3Subproblem 4
Set the factor '(3 + -1g)' equal to zero and attempt to solve: Simplifying 3 + -1g = 0 Solving 3 + -1g = 0 Move all terms containing g to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1g = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1g = 0 + -3 -1g = 0 + -3 Combine like terms: 0 + -3 = -3 -1g = -3 Divide each side by '-1'. g = 3 Simplifying g = 3Solution
g = {-3, 3, -3, 3}
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