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Simplifying g2 + 16g + 59 = 0 Reorder the terms: 59 + 16g + g2 = 0 Solving 59 + 16g + g2 = 0 Solving for variable 'g'. Begin completing the square. Move the constant term to the right: Add '-59' to each side of the equation. 59 + 16g + -59 + g2 = 0 + -59 Reorder the terms: 59 + -59 + 16g + g2 = 0 + -59 Combine like terms: 59 + -59 = 0 0 + 16g + g2 = 0 + -59 16g + g2 = 0 + -59 Combine like terms: 0 + -59 = -59 16g + g2 = -59 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 = -59 + 64 Reorder the terms: 64 + 16g + g2 = -59 + 64 Combine like terms: -59 + 64 = 5 64 + 16g + g2 = 5 Factor a perfect square on the left side: (g + 8)(g + 8) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (g + 8) equal to 2.236067978 and -2.236067978.Subproblem 1
g + 8 = 2.236067978 Simplifying g + 8 = 2.236067978 Reorder the terms: 8 + g = 2.236067978 Solving 8 + g = 2.236067978 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 = 2.236067978 + -8 Combine like terms: 8 + -8 = 0 0 + g = 2.236067978 + -8 g = 2.236067978 + -8 Combine like terms: 2.236067978 + -8 = -5.763932022 g = -5.763932022 Simplifying g = -5.763932022Subproblem 2
g + 8 = -2.236067978 Simplifying g + 8 = -2.236067978 Reorder the terms: 8 + g = -2.236067978 Solving 8 + g = -2.236067978 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 = -2.236067978 + -8 Combine like terms: 8 + -8 = 0 0 + g = -2.236067978 + -8 g = -2.236067978 + -8 Combine like terms: -2.236067978 + -8 = -10.236067978 g = -10.236067978 Simplifying g = -10.236067978Solution
The solution to the problem is based on the solutions from the subproblems. g = {-5.763932022, -10.236067978}
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