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Simplifying g2 + -2g + -47 = 0 Reorder the terms: -47 + -2g + g2 = 0 Solving -47 + -2g + g2 = 0 Solving for variable 'g'. Begin completing the square. Move the constant term to the right: Add '47' to each side of the equation. -47 + -2g + 47 + g2 = 0 + 47 Reorder the terms: -47 + 47 + -2g + g2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + -2g + g2 = 0 + 47 -2g + g2 = 0 + 47 Combine like terms: 0 + 47 = 47 -2g + g2 = 47 The g term is -2g. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2g + 1 + g2 = 47 + 1 Reorder the terms: 1 + -2g + g2 = 47 + 1 Combine like terms: 47 + 1 = 48 1 + -2g + g2 = 48 Factor a perfect square on the left side: (g + -1)(g + -1) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (g + -1) equal to 6.92820323 and -6.92820323.Subproblem 1
g + -1 = 6.92820323 Simplifying g + -1 = 6.92820323 Reorder the terms: -1 + g = 6.92820323 Solving -1 + g = 6.92820323 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + g = 6.92820323 + 1 Combine like terms: -1 + 1 = 0 0 + g = 6.92820323 + 1 g = 6.92820323 + 1 Combine like terms: 6.92820323 + 1 = 7.92820323 g = 7.92820323 Simplifying g = 7.92820323Subproblem 2
g + -1 = -6.92820323 Simplifying g + -1 = -6.92820323 Reorder the terms: -1 + g = -6.92820323 Solving -1 + g = -6.92820323 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + g = -6.92820323 + 1 Combine like terms: -1 + 1 = 0 0 + g = -6.92820323 + 1 g = -6.92820323 + 1 Combine like terms: -6.92820323 + 1 = -5.92820323 g = -5.92820323 Simplifying g = -5.92820323Solution
The solution to the problem is based on the solutions from the subproblems. g = {7.92820323, -5.92820323}
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