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Simplifying g2 + 2g + 0.4 = 0.9g2 Reorder the terms: 0.4 + 2g + g2 = 0.9g2 Solving 0.4 + 2g + g2 = 0.9g2 Solving for variable 'g'. Combine like terms: g2 + -0.9g2 = 0.1g2 0.4 + 2g + 0.1g2 = 0.9g2 + -0.9g2 Combine like terms: 0.9g2 + -0.9g2 = 0.0 0.4 + 2g + 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 + 20g + g2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + 20g + -4 + g2 = 0 + -4 Reorder the terms: 4 + -4 + 20g + g2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 20g + g2 = 0 + -4 20g + g2 = 0 + -4 Combine like terms: 0 + -4 = -4 20g + g2 = -4 The g term is 20g. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20g + 100 + g2 = -4 + 100 Reorder the terms: 100 + 20g + g2 = -4 + 100 Combine like terms: -4 + 100 = 96 100 + 20g + g2 = 96 Factor a perfect square on the left side: (g + 10)(g + 10) = 96 Calculate the square root of the right side: 9.797958971 Break this problem into two subproblems by setting (g + 10) equal to 9.797958971 and -9.797958971.Subproblem 1
g + 10 = 9.797958971 Simplifying g + 10 = 9.797958971 Reorder the terms: 10 + g = 9.797958971 Solving 10 + g = 9.797958971 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + g = 9.797958971 + -10 Combine like terms: 10 + -10 = 0 0 + g = 9.797958971 + -10 g = 9.797958971 + -10 Combine like terms: 9.797958971 + -10 = -0.202041029 g = -0.202041029 Simplifying g = -0.202041029Subproblem 2
g + 10 = -9.797958971 Simplifying g + 10 = -9.797958971 Reorder the terms: 10 + g = -9.797958971 Solving 10 + g = -9.797958971 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + g = -9.797958971 + -10 Combine like terms: 10 + -10 = 0 0 + g = -9.797958971 + -10 g = -9.797958971 + -10 Combine like terms: -9.797958971 + -10 = -19.797958971 g = -19.797958971 Simplifying g = -19.797958971Solution
The solution to the problem is based on the solutions from the subproblems. g = {-0.202041029, -19.797958971}
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