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Simplifying g2 + 0.66g + 0.011 = 0 Reorder the terms: 0.011 + 0.66g + g2 = 0 Solving 0.011 + 0.66g + g2 = 0 Solving for variable 'g'. Begin completing the square. Move the constant term to the right: Add '-0.011' to each side of the equation. 0.011 + 0.66g + -0.011 + g2 = 0 + -0.011 Reorder the terms: 0.011 + -0.011 + 0.66g + g2 = 0 + -0.011 Combine like terms: 0.011 + -0.011 = 0.000 0.000 + 0.66g + g2 = 0 + -0.011 0.66g + g2 = 0 + -0.011 Combine like terms: 0 + -0.011 = -0.011 0.66g + g2 = -0.011 The g term is 0.66g. Take half its coefficient (0.33). Square it (0.1089) and add it to both sides. Add '0.1089' to each side of the equation. 0.66g + 0.1089 + g2 = -0.011 + 0.1089 Reorder the terms: 0.1089 + 0.66g + g2 = -0.011 + 0.1089 Combine like terms: -0.011 + 0.1089 = 0.0979 0.1089 + 0.66g + g2 = 0.0979 Factor a perfect square on the left side: (g + 0.33)(g + 0.33) = 0.0979 Calculate the square root of the right side: 0.312889757 Break this problem into two subproblems by setting (g + 0.33) equal to 0.312889757 and -0.312889757.Subproblem 1
g + 0.33 = 0.312889757 Simplifying g + 0.33 = 0.312889757 Reorder the terms: 0.33 + g = 0.312889757 Solving 0.33 + g = 0.312889757 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-0.33' to each side of the equation. 0.33 + -0.33 + g = 0.312889757 + -0.33 Combine like terms: 0.33 + -0.33 = 0.00 0.00 + g = 0.312889757 + -0.33 g = 0.312889757 + -0.33 Combine like terms: 0.312889757 + -0.33 = -0.017110243 g = -0.017110243 Simplifying g = -0.017110243Subproblem 2
g + 0.33 = -0.312889757 Simplifying g + 0.33 = -0.312889757 Reorder the terms: 0.33 + g = -0.312889757 Solving 0.33 + g = -0.312889757 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-0.33' to each side of the equation. 0.33 + -0.33 + g = -0.312889757 + -0.33 Combine like terms: 0.33 + -0.33 = 0.00 0.00 + g = -0.312889757 + -0.33 g = -0.312889757 + -0.33 Combine like terms: -0.312889757 + -0.33 = -0.642889757 g = -0.642889757 Simplifying g = -0.642889757Solution
The solution to the problem is based on the solutions from the subproblems. g = {-0.017110243, -0.642889757}
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