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Simplifying g2 + 18g = 48 Reorder the terms: 18g + g2 = 48 Solving 18g + g2 = 48 Solving for variable 'g'. Reorder the terms: -48 + 18g + g2 = 48 + -48 Combine like terms: 48 + -48 = 0 -48 + 18g + g2 = 0 Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + 18g + 48 + g2 = 0 + 48 Reorder the terms: -48 + 48 + 18g + g2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 18g + g2 = 0 + 48 18g + g2 = 0 + 48 Combine like terms: 0 + 48 = 48 18g + g2 = 48 The g term is 18g. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18g + 81 + g2 = 48 + 81 Reorder the terms: 81 + 18g + g2 = 48 + 81 Combine like terms: 48 + 81 = 129 81 + 18g + g2 = 129 Factor a perfect square on the left side: (g + 9)(g + 9) = 129 Calculate the square root of the right side: 11.357816692 Break this problem into two subproblems by setting (g + 9) equal to 11.357816692 and -11.357816692.Subproblem 1
g + 9 = 11.357816692 Simplifying g + 9 = 11.357816692 Reorder the terms: 9 + g = 11.357816692 Solving 9 + g = 11.357816692 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + g = 11.357816692 + -9 Combine like terms: 9 + -9 = 0 0 + g = 11.357816692 + -9 g = 11.357816692 + -9 Combine like terms: 11.357816692 + -9 = 2.357816692 g = 2.357816692 Simplifying g = 2.357816692Subproblem 2
g + 9 = -11.357816692 Simplifying g + 9 = -11.357816692 Reorder the terms: 9 + g = -11.357816692 Solving 9 + g = -11.357816692 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + g = -11.357816692 + -9 Combine like terms: 9 + -9 = 0 0 + g = -11.357816692 + -9 g = -11.357816692 + -9 Combine like terms: -11.357816692 + -9 = -20.357816692 g = -20.357816692 Simplifying g = -20.357816692Solution
The solution to the problem is based on the solutions from the subproblems. g = {2.357816692, -20.357816692}
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