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Simplifying g2 + -14g = -10 Reorder the terms: -14g + g2 = -10 Solving -14g + g2 = -10 Solving for variable 'g'. Reorder the terms: 10 + -14g + g2 = -10 + 10 Combine like terms: -10 + 10 = 0 10 + -14g + g2 = 0 Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + -14g + -10 + g2 = 0 + -10 Reorder the terms: 10 + -10 + -14g + g2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -14g + g2 = 0 + -10 -14g + g2 = 0 + -10 Combine like terms: 0 + -10 = -10 -14g + g2 = -10 The g term is -14g. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14g + 49 + g2 = -10 + 49 Reorder the terms: 49 + -14g + g2 = -10 + 49 Combine like terms: -10 + 49 = 39 49 + -14g + g2 = 39 Factor a perfect square on the left side: (g + -7)(g + -7) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (g + -7) equal to 6.244997998 and -6.244997998.Subproblem 1
g + -7 = 6.244997998 Simplifying g + -7 = 6.244997998 Reorder the terms: -7 + g = 6.244997998 Solving -7 + g = 6.244997998 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + g = 6.244997998 + 7 Combine like terms: -7 + 7 = 0 0 + g = 6.244997998 + 7 g = 6.244997998 + 7 Combine like terms: 6.244997998 + 7 = 13.244997998 g = 13.244997998 Simplifying g = 13.244997998Subproblem 2
g + -7 = -6.244997998 Simplifying g + -7 = -6.244997998 Reorder the terms: -7 + g = -6.244997998 Solving -7 + g = -6.244997998 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + g = -6.244997998 + 7 Combine like terms: -7 + 7 = 0 0 + g = -6.244997998 + 7 g = -6.244997998 + 7 Combine like terms: -6.244997998 + 7 = 0.755002002 g = 0.755002002 Simplifying g = 0.755002002Solution
The solution to the problem is based on the solutions from the subproblems. g = {13.244997998, 0.755002002}
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