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Simplifying -7g2 + 7g + 8 = 0 Reorder the terms: 8 + 7g + -7g2 = 0 Solving 8 + 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'. -1.142857143 + -1g + g2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + -1g + 1.142857143 + g2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + -1g + g2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + -1g + g2 = 0 + 1.142857143 -1g + g2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 -1g + g2 = 1.142857143 The g term is -1g. 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. -1g + 0.25 + g2 = 1.142857143 + 0.25 Reorder the terms: 0.25 + -1g + g2 = 1.142857143 + 0.25 Combine like terms: 1.142857143 + 0.25 = 1.392857143 0.25 + -1g + g2 = 1.392857143 Factor a perfect square on the left side: (g + -0.5)(g + -0.5) = 1.392857143 Calculate the square root of the right side: 1.180193689 Break this problem into two subproblems by setting (g + -0.5) equal to 1.180193689 and -1.180193689.Subproblem 1
g + -0.5 = 1.180193689 Simplifying g + -0.5 = 1.180193689 Reorder the terms: -0.5 + g = 1.180193689 Solving -0.5 + g = 1.180193689 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 = 1.180193689 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + g = 1.180193689 + 0.5 g = 1.180193689 + 0.5 Combine like terms: 1.180193689 + 0.5 = 1.680193689 g = 1.680193689 Simplifying g = 1.680193689Subproblem 2
g + -0.5 = -1.180193689 Simplifying g + -0.5 = -1.180193689 Reorder the terms: -0.5 + g = -1.180193689 Solving -0.5 + g = -1.180193689 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 = -1.180193689 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + g = -1.180193689 + 0.5 g = -1.180193689 + 0.5 Combine like terms: -1.180193689 + 0.5 = -0.680193689 g = -0.680193689 Simplifying g = -0.680193689Solution
The solution to the problem is based on the solutions from the subproblems. g = {1.680193689, -0.680193689}
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