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Simplifying 9(2 + g) * g = 6 Reorder the terms for easier multiplication: 9g(2 + g) = 6 (2 * 9g + g * 9g) = 6 (18g + 9g2) = 6 Solving 18g + 9g2 = 6 Solving for variable 'g'. Reorder the terms: -6 + 18g + 9g2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 18g + 9g2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-2 + 6g + 3g2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + 6g + 3g2)' equal to zero and attempt to solve: Simplifying -2 + 6g + 3g2 = 0 Solving -2 + 6g + 3g2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.6666666667 + 2g + g2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + 2g + 0.6666666667 + g2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + 2g + g2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + 2g + g2 = 0 + 0.6666666667 2g + g2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 2g + g2 = 0.6666666667 The g term is 2g. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2g + 1 + g2 = 0.6666666667 + 1 Reorder the terms: 1 + 2g + g2 = 0.6666666667 + 1 Combine like terms: 0.6666666667 + 1 = 1.6666666667 1 + 2g + g2 = 1.6666666667 Factor a perfect square on the left side: (g + 1)(g + 1) = 1.6666666667 Calculate the square root of the right side: 1.290994449 Break this problem into two subproblems by setting (g + 1) equal to 1.290994449 and -1.290994449.Subproblem 1
g + 1 = 1.290994449 Simplifying g + 1 = 1.290994449 Reorder the terms: 1 + g = 1.290994449 Solving 1 + g = 1.290994449 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + g = 1.290994449 + -1 Combine like terms: 1 + -1 = 0 0 + g = 1.290994449 + -1 g = 1.290994449 + -1 Combine like terms: 1.290994449 + -1 = 0.290994449 g = 0.290994449 Simplifying g = 0.290994449Subproblem 2
g + 1 = -1.290994449 Simplifying g + 1 = -1.290994449 Reorder the terms: 1 + g = -1.290994449 Solving 1 + g = -1.290994449 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + g = -1.290994449 + -1 Combine like terms: 1 + -1 = 0 0 + g = -1.290994449 + -1 g = -1.290994449 + -1 Combine like terms: -1.290994449 + -1 = -2.290994449 g = -2.290994449 Simplifying g = -2.290994449Solution
The solution to the problem is based on the solutions from the subproblems. g = {0.290994449, -2.290994449}Solution
g = {0.290994449, -2.290994449}
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