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Simplifying 2g2 + -8g + 1 = 0 Reorder the terms: 1 + -8g + 2g2 = 0 Solving 1 + -8g + 2g2 = 0 Solving for variable 'g'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + -4g + g2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -4g + -0.5 + g2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -4g + g2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -4g + g2 = 0 + -0.5 -4g + g2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -4g + g2 = -0.5 The g term is -4g. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4g + 4 + g2 = -0.5 + 4 Reorder the terms: 4 + -4g + g2 = -0.5 + 4 Combine like terms: -0.5 + 4 = 3.5 4 + -4g + g2 = 3.5 Factor a perfect square on the left side: (g + -2)(g + -2) = 3.5 Calculate the square root of the right side: 1.870828693 Break this problem into two subproblems by setting (g + -2) equal to 1.870828693 and -1.870828693.Subproblem 1
g + -2 = 1.870828693 Simplifying g + -2 = 1.870828693 Reorder the terms: -2 + g = 1.870828693 Solving -2 + g = 1.870828693 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + g = 1.870828693 + 2 Combine like terms: -2 + 2 = 0 0 + g = 1.870828693 + 2 g = 1.870828693 + 2 Combine like terms: 1.870828693 + 2 = 3.870828693 g = 3.870828693 Simplifying g = 3.870828693Subproblem 2
g + -2 = -1.870828693 Simplifying g + -2 = -1.870828693 Reorder the terms: -2 + g = -1.870828693 Solving -2 + g = -1.870828693 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + g = -1.870828693 + 2 Combine like terms: -2 + 2 = 0 0 + g = -1.870828693 + 2 g = -1.870828693 + 2 Combine like terms: -1.870828693 + 2 = 0.129171307 g = 0.129171307 Simplifying g = 0.129171307Solution
The solution to the problem is based on the solutions from the subproblems. g = {3.870828693, 0.129171307}
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