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Simplifying g2 + -16g + 30 = 0 Reorder the terms: 30 + -16g + g2 = 0 Solving 30 + -16g + g2 = 0 Solving for variable 'g'. Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + -16g + -30 + g2 = 0 + -30 Reorder the terms: 30 + -30 + -16g + g2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -16g + g2 = 0 + -30 -16g + g2 = 0 + -30 Combine like terms: 0 + -30 = -30 -16g + g2 = -30 The g term is -16g. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16g + 64 + g2 = -30 + 64 Reorder the terms: 64 + -16g + g2 = -30 + 64 Combine like terms: -30 + 64 = 34 64 + -16g + g2 = 34 Factor a perfect square on the left side: (g + -8)(g + -8) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (g + -8) equal to 5.830951895 and -5.830951895.Subproblem 1
g + -8 = 5.830951895 Simplifying g + -8 = 5.830951895 Reorder the terms: -8 + g = 5.830951895 Solving -8 + g = 5.830951895 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + g = 5.830951895 + 8 Combine like terms: -8 + 8 = 0 0 + g = 5.830951895 + 8 g = 5.830951895 + 8 Combine like terms: 5.830951895 + 8 = 13.830951895 g = 13.830951895 Simplifying g = 13.830951895Subproblem 2
g + -8 = -5.830951895 Simplifying g + -8 = -5.830951895 Reorder the terms: -8 + g = -5.830951895 Solving -8 + g = -5.830951895 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + g = -5.830951895 + 8 Combine like terms: -8 + 8 = 0 0 + g = -5.830951895 + 8 g = -5.830951895 + 8 Combine like terms: -5.830951895 + 8 = 2.169048105 g = 2.169048105 Simplifying g = 2.169048105Solution
The solution to the problem is based on the solutions from the subproblems. g = {13.830951895, 2.169048105}
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