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Simplifying 9g + 5 = 6g2 Reorder the terms: 5 + 9g = 6g2 Solving 5 + 9g = 6g2 Solving for variable 'g'. Combine like terms: 6g2 + -6g2 = 0 5 + 9g + -6g2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -0.8333333333 + -1.5g + g2 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + -1.5g + 0.8333333333 + g2 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + -1.5g + g2 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + -1.5g + g2 = 0 + 0.8333333333 -1.5g + g2 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 -1.5g + g2 = 0.8333333333 The g term is -1.5g. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5g + 0.5625 + g2 = 0.8333333333 + 0.5625 Reorder the terms: 0.5625 + -1.5g + g2 = 0.8333333333 + 0.5625 Combine like terms: 0.8333333333 + 0.5625 = 1.3958333333 0.5625 + -1.5g + g2 = 1.3958333333 Factor a perfect square on the left side: (g + -0.75)(g + -0.75) = 1.3958333333 Calculate the square root of the right side: 1.181453907 Break this problem into two subproblems by setting (g + -0.75) equal to 1.181453907 and -1.181453907.Subproblem 1
g + -0.75 = 1.181453907 Simplifying g + -0.75 = 1.181453907 Reorder the terms: -0.75 + g = 1.181453907 Solving -0.75 + g = 1.181453907 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + g = 1.181453907 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + g = 1.181453907 + 0.75 g = 1.181453907 + 0.75 Combine like terms: 1.181453907 + 0.75 = 1.931453907 g = 1.931453907 Simplifying g = 1.931453907Subproblem 2
g + -0.75 = -1.181453907 Simplifying g + -0.75 = -1.181453907 Reorder the terms: -0.75 + g = -1.181453907 Solving -0.75 + g = -1.181453907 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + g = -1.181453907 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + g = -1.181453907 + 0.75 g = -1.181453907 + 0.75 Combine like terms: -1.181453907 + 0.75 = -0.431453907 g = -0.431453907 Simplifying g = -0.431453907Solution
The solution to the problem is based on the solutions from the subproblems. g = {1.931453907, -0.431453907}
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