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Simplifying 5g5 + -10g3 + -15g = 0 Reorder the terms: -15g + -10g3 + 5g5 = 0 Solving -15g + -10g3 + 5g5 = 0 Solving for variable 'g'. Factor out the Greatest Common Factor (GCF), '5g'. 5g(-3 + -2g2 + g4) = 0 Factor a trinomial. 5g((-1 + -1g2)(3 + -1g2)) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'g' equal to zero and attempt to solve: Simplifying g = 0 Solving g = 0 Move all terms containing g to the left, all other terms to the right. Simplifying g = 0Subproblem 2
Set the factor '(-1 + -1g2)' equal to zero and attempt to solve: Simplifying -1 + -1g2 = 0 Solving -1 + -1g2 = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1g2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1g2 = 0 + 1 -1g2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1g2 = 1 Divide each side by '-1'. g2 = -1 Simplifying g2 = -1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(3 + -1g2)' equal to zero and attempt to solve: Simplifying 3 + -1g2 = 0 Solving 3 + -1g2 = 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 + -1g2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1g2 = 0 + -3 -1g2 = 0 + -3 Combine like terms: 0 + -3 = -3 -1g2 = -3 Divide each side by '-1'. g2 = 3 Simplifying g2 = 3 Take the square root of each side: g = {-1.732050808, 1.732050808}Solution
g = {0, -1.732050808, 1.732050808}
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