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Simplifying g2 + -1g + -20 = 20 Reorder the terms: -20 + -1g + g2 = 20 Solving -20 + -1g + g2 = 20 Solving for variable 'g'. Reorder the terms: -20 + -20 + -1g + g2 = 20 + -20 Combine like terms: -20 + -20 = -40 -40 + -1g + g2 = 20 + -20 Combine like terms: 20 + -20 = 0 -40 + -1g + g2 = 0 Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + -1g + 40 + g2 = 0 + 40 Reorder the terms: -40 + 40 + -1g + g2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -1g + g2 = 0 + 40 -1g + g2 = 0 + 40 Combine like terms: 0 + 40 = 40 -1g + g2 = 40 The g term is -1g. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1g + 0.25 + g2 = 40 + 0.25 Reorder the terms: 0.25 + -1g + g2 = 40 + 0.25 Combine like terms: 40 + 0.25 = 40.25 0.25 + -1g + g2 = 40.25 Factor a perfect square on the left side: (g + -0.5)(g + -0.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (g + -0.5) equal to 6.34428877 and -6.34428877.Subproblem 1
g + -0.5 = 6.34428877 Simplifying g + -0.5 = 6.34428877 Reorder the terms: -0.5 + g = 6.34428877 Solving -0.5 + g = 6.34428877 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + g = 6.34428877 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + g = 6.34428877 + 0.5 g = 6.34428877 + 0.5 Combine like terms: 6.34428877 + 0.5 = 6.84428877 g = 6.84428877 Simplifying g = 6.84428877Subproblem 2
g + -0.5 = -6.34428877 Simplifying g + -0.5 = -6.34428877 Reorder the terms: -0.5 + g = -6.34428877 Solving -0.5 + g = -6.34428877 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + g = -6.34428877 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + g = -6.34428877 + 0.5 g = -6.34428877 + 0.5 Combine like terms: -6.34428877 + 0.5 = -5.84428877 g = -5.84428877 Simplifying g = -5.84428877Solution
The solution to the problem is based on the solutions from the subproblems. g = {6.84428877, -5.84428877}
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