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Simplifying 7g2 + 2g + -3 = 0 Reorder the terms: -3 + 2g + 7g2 = 0 Solving -3 + 2g + 7g2 = 0 Solving for variable 'g'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.4285714286 + 0.2857142857g + g2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.2857142857g + 0.4285714286 + g2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + 0.2857142857g + g2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + 0.2857142857g + g2 = 0 + 0.4285714286 0.2857142857g + g2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 0.2857142857g + g2 = 0.4285714286 The g term is 0.2857142857g. Take half its coefficient (0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. 0.2857142857g + 0.02040816328 + g2 = 0.4285714286 + 0.02040816328 Reorder the terms: 0.02040816328 + 0.2857142857g + g2 = 0.4285714286 + 0.02040816328 Combine like terms: 0.4285714286 + 0.02040816328 = 0.44897959188 0.02040816328 + 0.2857142857g + g2 = 0.44897959188 Factor a perfect square on the left side: (g + 0.1428571429)(g + 0.1428571429) = 0.44897959188 Calculate the square root of the right side: 0.670059394 Break this problem into two subproblems by setting (g + 0.1428571429) equal to 0.670059394 and -0.670059394.Subproblem 1
g + 0.1428571429 = 0.670059394 Simplifying g + 0.1428571429 = 0.670059394 Reorder the terms: 0.1428571429 + g = 0.670059394 Solving 0.1428571429 + g = 0.670059394 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + g = 0.670059394 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + g = 0.670059394 + -0.1428571429 g = 0.670059394 + -0.1428571429 Combine like terms: 0.670059394 + -0.1428571429 = 0.5272022511 g = 0.5272022511 Simplifying g = 0.5272022511Subproblem 2
g + 0.1428571429 = -0.670059394 Simplifying g + 0.1428571429 = -0.670059394 Reorder the terms: 0.1428571429 + g = -0.670059394 Solving 0.1428571429 + g = -0.670059394 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + g = -0.670059394 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + g = -0.670059394 + -0.1428571429 g = -0.670059394 + -0.1428571429 Combine like terms: -0.670059394 + -0.1428571429 = -0.8129165369 g = -0.8129165369 Simplifying g = -0.8129165369Solution
The solution to the problem is based on the solutions from the subproblems. g = {0.5272022511, -0.8129165369}
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