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Simplifying g2 + -28g + 39 = 0 Reorder the terms: 39 + -28g + g2 = 0 Solving 39 + -28g + g2 = 0 Solving for variable 'g'. Begin completing the square. Move the constant term to the right: Add '-39' to each side of the equation. 39 + -28g + -39 + g2 = 0 + -39 Reorder the terms: 39 + -39 + -28g + g2 = 0 + -39 Combine like terms: 39 + -39 = 0 0 + -28g + g2 = 0 + -39 -28g + g2 = 0 + -39 Combine like terms: 0 + -39 = -39 -28g + g2 = -39 The g term is -28g. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28g + 196 + g2 = -39 + 196 Reorder the terms: 196 + -28g + g2 = -39 + 196 Combine like terms: -39 + 196 = 157 196 + -28g + g2 = 157 Factor a perfect square on the left side: (g + -14)(g + -14) = 157 Calculate the square root of the right side: 12.529964086 Break this problem into two subproblems by setting (g + -14) equal to 12.529964086 and -12.529964086.Subproblem 1
g + -14 = 12.529964086 Simplifying g + -14 = 12.529964086 Reorder the terms: -14 + g = 12.529964086 Solving -14 + g = 12.529964086 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + g = 12.529964086 + 14 Combine like terms: -14 + 14 = 0 0 + g = 12.529964086 + 14 g = 12.529964086 + 14 Combine like terms: 12.529964086 + 14 = 26.529964086 g = 26.529964086 Simplifying g = 26.529964086Subproblem 2
g + -14 = -12.529964086 Simplifying g + -14 = -12.529964086 Reorder the terms: -14 + g = -12.529964086 Solving -14 + g = -12.529964086 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + g = -12.529964086 + 14 Combine like terms: -14 + 14 = 0 0 + g = -12.529964086 + 14 g = -12.529964086 + 14 Combine like terms: -12.529964086 + 14 = 1.470035914 g = 1.470035914 Simplifying g = 1.470035914Solution
The solution to the problem is based on the solutions from the subproblems. g = {26.529964086, 1.470035914}
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