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Simplifying g2 + 6g + 4 = 0 Reorder the terms: 4 + 6g + g2 = 0 Solving 4 + 6g + g2 = 0 Solving for variable 'g'. Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 6g + -4 + g2 = 0 + -4 Reorder the terms: 4 + -4 + 6g + g2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 6g + g2 = 0 + -4 6g + g2 = 0 + -4 Combine like terms: 0 + -4 = -4 6g + g2 = -4 The g term is 6g. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6g + 9 + g2 = -4 + 9 Reorder the terms: 9 + 6g + g2 = -4 + 9 Combine like terms: -4 + 9 = 5 9 + 6g + g2 = 5 Factor a perfect square on the left side: (g + 3)(g + 3) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (g + 3) equal to 2.236067978 and -2.236067978.Subproblem 1
g + 3 = 2.236067978 Simplifying g + 3 = 2.236067978 Reorder the terms: 3 + g = 2.236067978 Solving 3 + g = 2.236067978 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + g = 2.236067978 + -3 Combine like terms: 3 + -3 = 0 0 + g = 2.236067978 + -3 g = 2.236067978 + -3 Combine like terms: 2.236067978 + -3 = -0.763932022 g = -0.763932022 Simplifying g = -0.763932022Subproblem 2
g + 3 = -2.236067978 Simplifying g + 3 = -2.236067978 Reorder the terms: 3 + g = -2.236067978 Solving 3 + g = -2.236067978 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + g = -2.236067978 + -3 Combine like terms: 3 + -3 = 0 0 + g = -2.236067978 + -3 g = -2.236067978 + -3 Combine like terms: -2.236067978 + -3 = -5.236067978 g = -5.236067978 Simplifying g = -5.236067978Solution
The solution to the problem is based on the solutions from the subproblems. g = {-0.763932022, -5.236067978}
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