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Simplifying g2 + -8g + 11 = 0 Reorder the terms: 11 + -8g + g2 = 0 Solving 11 + -8g + g2 = 0 Solving for variable 'g'. Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + -8g + -11 + g2 = 0 + -11 Reorder the terms: 11 + -11 + -8g + g2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -8g + g2 = 0 + -11 -8g + g2 = 0 + -11 Combine like terms: 0 + -11 = -11 -8g + g2 = -11 The g term is -8g. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8g + 16 + g2 = -11 + 16 Reorder the terms: 16 + -8g + g2 = -11 + 16 Combine like terms: -11 + 16 = 5 16 + -8g + g2 = 5 Factor a perfect square on the left side: (g + -4)(g + -4) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (g + -4) equal to 2.236067978 and -2.236067978.Subproblem 1
g + -4 = 2.236067978 Simplifying g + -4 = 2.236067978 Reorder the terms: -4 + g = 2.236067978 Solving -4 + g = 2.236067978 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + g = 2.236067978 + 4 Combine like terms: -4 + 4 = 0 0 + g = 2.236067978 + 4 g = 2.236067978 + 4 Combine like terms: 2.236067978 + 4 = 6.236067978 g = 6.236067978 Simplifying g = 6.236067978Subproblem 2
g + -4 = -2.236067978 Simplifying g + -4 = -2.236067978 Reorder the terms: -4 + g = -2.236067978 Solving -4 + g = -2.236067978 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + g = -2.236067978 + 4 Combine like terms: -4 + 4 = 0 0 + g = -2.236067978 + 4 g = -2.236067978 + 4 Combine like terms: -2.236067978 + 4 = 1.763932022 g = 1.763932022 Simplifying g = 1.763932022Solution
The solution to the problem is based on the solutions from the subproblems. g = {6.236067978, 1.763932022}
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