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Simplifying g2 + -16g + 22 = 0 Reorder the terms: 22 + -16g + g2 = 0 Solving 22 + -16g + g2 = 0 Solving for variable 'g'. Begin completing the square. Move the constant term to the right: Add '-22' to each side of the equation. 22 + -16g + -22 + g2 = 0 + -22 Reorder the terms: 22 + -22 + -16g + g2 = 0 + -22 Combine like terms: 22 + -22 = 0 0 + -16g + g2 = 0 + -22 -16g + g2 = 0 + -22 Combine like terms: 0 + -22 = -22 -16g + g2 = -22 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 = -22 + 64 Reorder the terms: 64 + -16g + g2 = -22 + 64 Combine like terms: -22 + 64 = 42 64 + -16g + g2 = 42 Factor a perfect square on the left side: (g + -8)(g + -8) = 42 Calculate the square root of the right side: 6.480740698 Break this problem into two subproblems by setting (g + -8) equal to 6.480740698 and -6.480740698.Subproblem 1
g + -8 = 6.480740698 Simplifying g + -8 = 6.480740698 Reorder the terms: -8 + g = 6.480740698 Solving -8 + g = 6.480740698 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 = 6.480740698 + 8 Combine like terms: -8 + 8 = 0 0 + g = 6.480740698 + 8 g = 6.480740698 + 8 Combine like terms: 6.480740698 + 8 = 14.480740698 g = 14.480740698 Simplifying g = 14.480740698Subproblem 2
g + -8 = -6.480740698 Simplifying g + -8 = -6.480740698 Reorder the terms: -8 + g = -6.480740698 Solving -8 + g = -6.480740698 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 = -6.480740698 + 8 Combine like terms: -8 + 8 = 0 0 + g = -6.480740698 + 8 g = -6.480740698 + 8 Combine like terms: -6.480740698 + 8 = 1.519259302 g = 1.519259302 Simplifying g = 1.519259302Solution
The solution to the problem is based on the solutions from the subproblems. g = {14.480740698, 1.519259302}
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