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Simplifying g2 + g + -38 = 0 Reorder the terms: -38 + g + g2 = 0 Solving -38 + g + g2 = 0 Solving for variable 'g'. Begin completing the square. Move the constant term to the right: Add '38' to each side of the equation. -38 + g + 38 + g2 = 0 + 38 Reorder the terms: -38 + 38 + g + g2 = 0 + 38 Combine like terms: -38 + 38 = 0 0 + g + g2 = 0 + 38 g + g2 = 0 + 38 Combine like terms: 0 + 38 = 38 g + g2 = 38 The g term is g. 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. g + 0.25 + g2 = 38 + 0.25 Reorder the terms: 0.25 + g + g2 = 38 + 0.25 Combine like terms: 38 + 0.25 = 38.25 0.25 + g + g2 = 38.25 Factor a perfect square on the left side: (g + 0.5)(g + 0.5) = 38.25 Calculate the square root of the right side: 6.184658438 Break this problem into two subproblems by setting (g + 0.5) equal to 6.184658438 and -6.184658438.Subproblem 1
g + 0.5 = 6.184658438 Simplifying g + 0.5 = 6.184658438 Reorder the terms: 0.5 + g = 6.184658438 Solving 0.5 + g = 6.184658438 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 = 6.184658438 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + g = 6.184658438 + -0.5 g = 6.184658438 + -0.5 Combine like terms: 6.184658438 + -0.5 = 5.684658438 g = 5.684658438 Simplifying g = 5.684658438Subproblem 2
g + 0.5 = -6.184658438 Simplifying g + 0.5 = -6.184658438 Reorder the terms: 0.5 + g = -6.184658438 Solving 0.5 + g = -6.184658438 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 = -6.184658438 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + g = -6.184658438 + -0.5 g = -6.184658438 + -0.5 Combine like terms: -6.184658438 + -0.5 = -6.684658438 g = -6.684658438 Simplifying g = -6.684658438Solution
The solution to the problem is based on the solutions from the subproblems. g = {5.684658438, -6.684658438}
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