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Simplifying g2 + 2g + 0.4 = 0.9g2 + g Reorder the terms: 0.4 + 2g + g2 = 0.9g2 + g Reorder the terms: 0.4 + 2g + g2 = g + 0.9g2 Solving 0.4 + 2g + g2 = g + 0.9g2 Solving for variable 'g'. Reorder the terms: 0.4 + 2g + -1g + g2 + -0.9g2 = g + 0.9g2 + -1g + -0.9g2 Combine like terms: 2g + -1g = 1g 0.4 + 1g + g2 + -0.9g2 = g + 0.9g2 + -1g + -0.9g2 Combine like terms: g2 + -0.9g2 = 0.1g2 0.4 + 1g + 0.1g2 = g + 0.9g2 + -1g + -0.9g2 Reorder the terms: 0.4 + 1g + 0.1g2 = g + -1g + 0.9g2 + -0.9g2 Combine like terms: g + -1g = 0 0.4 + 1g + 0.1g2 = 0 + 0.9g2 + -0.9g2 0.4 + 1g + 0.1g2 = 0.9g2 + -0.9g2 Combine like terms: 0.9g2 + -0.9g2 = 0.0 0.4 + 1g + 0.1g2 = 0.0 Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. 4 + 10g + g2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + 10g + -4 + g2 = 0 + -4 Reorder the terms: 4 + -4 + 10g + g2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 10g + g2 = 0 + -4 10g + g2 = 0 + -4 Combine like terms: 0 + -4 = -4 10g + g2 = -4 The g term is 10g. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10g + 25 + g2 = -4 + 25 Reorder the terms: 25 + 10g + g2 = -4 + 25 Combine like terms: -4 + 25 = 21 25 + 10g + g2 = 21 Factor a perfect square on the left side: (g + 5)(g + 5) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (g + 5) equal to 4.582575695 and -4.582575695.Subproblem 1
g + 5 = 4.582575695 Simplifying g + 5 = 4.582575695 Reorder the terms: 5 + g = 4.582575695 Solving 5 + g = 4.582575695 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + g = 4.582575695 + -5 Combine like terms: 5 + -5 = 0 0 + g = 4.582575695 + -5 g = 4.582575695 + -5 Combine like terms: 4.582575695 + -5 = -0.417424305 g = -0.417424305 Simplifying g = -0.417424305Subproblem 2
g + 5 = -4.582575695 Simplifying g + 5 = -4.582575695 Reorder the terms: 5 + g = -4.582575695 Solving 5 + g = -4.582575695 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + g = -4.582575695 + -5 Combine like terms: 5 + -5 = 0 0 + g = -4.582575695 + -5 g = -4.582575695 + -5 Combine like terms: -4.582575695 + -5 = -9.582575695 g = -9.582575695 Simplifying g = -9.582575695Solution
The solution to the problem is based on the solutions from the subproblems. g = {-0.417424305, -9.582575695}
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