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Simplifying 7g2 + 7g + -5 = 0 Reorder the terms: -5 + 7g + 7g2 = 0 Solving -5 + 7g + 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'. -0.7142857143 + g + g2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + g + 0.7142857143 + g2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + g + g2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + g + g2 = 0 + 0.7142857143 g + g2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 g + g2 = 0.7142857143 The g term is g. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + g2 = 0.7142857143 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + g2 = 0.7142857143 + 0.25 Combine like terms: 0.7142857143 + 0.25 = 0.9642857143 1.25 + g2 = 0.9642857143 Factor a perfect square on the left side: (g + 0.5)(g + 0.5) = 0.9642857143 Calculate the square root of the right side: 0.981980506 Break this problem into two subproblems by setting (g + 0.5) equal to 0.981980506 and -0.981980506.Subproblem 1
g + 0.5 = 0.981980506 Simplifying g + 0.5 = 0.981980506 Reorder the terms: 0.5 + g = 0.981980506 Solving 0.5 + g = 0.981980506 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + g = 0.981980506 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + g = 0.981980506 + -0.5 g = 0.981980506 + -0.5 Combine like terms: 0.981980506 + -0.5 = 0.481980506 g = 0.481980506 Simplifying g = 0.481980506Subproblem 2
g + 0.5 = -0.981980506 Simplifying g + 0.5 = -0.981980506 Reorder the terms: 0.5 + g = -0.981980506 Solving 0.5 + g = -0.981980506 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + g = -0.981980506 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + g = -0.981980506 + -0.5 g = -0.981980506 + -0.5 Combine like terms: -0.981980506 + -0.5 = -1.481980506 g = -1.481980506 Simplifying g = -1.481980506Solution
The solution to the problem is based on the solutions from the subproblems. g = {0.481980506, -1.481980506}
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