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Simplifying g2 + 29g + -43 = 0 Reorder the terms: -43 + 29g + g2 = 0 Solving -43 + 29g + g2 = 0 Solving for variable 'g'. Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + 29g + 43 + g2 = 0 + 43 Reorder the terms: -43 + 43 + 29g + g2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + 29g + g2 = 0 + 43 29g + g2 = 0 + 43 Combine like terms: 0 + 43 = 43 29g + g2 = 43 The g term is 29g. Take half its coefficient (14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. 29g + 210.25 + g2 = 43 + 210.25 Reorder the terms: 210.25 + 29g + g2 = 43 + 210.25 Combine like terms: 43 + 210.25 = 253.25 210.25 + 29g + g2 = 253.25 Factor a perfect square on the left side: (g + 14.5)(g + 14.5) = 253.25 Calculate the square root of the right side: 15.913830463 Break this problem into two subproblems by setting (g + 14.5) equal to 15.913830463 and -15.913830463.Subproblem 1
g + 14.5 = 15.913830463 Simplifying g + 14.5 = 15.913830463 Reorder the terms: 14.5 + g = 15.913830463 Solving 14.5 + g = 15.913830463 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + g = 15.913830463 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + g = 15.913830463 + -14.5 g = 15.913830463 + -14.5 Combine like terms: 15.913830463 + -14.5 = 1.413830463 g = 1.413830463 Simplifying g = 1.413830463Subproblem 2
g + 14.5 = -15.913830463 Simplifying g + 14.5 = -15.913830463 Reorder the terms: 14.5 + g = -15.913830463 Solving 14.5 + g = -15.913830463 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + g = -15.913830463 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + g = -15.913830463 + -14.5 g = -15.913830463 + -14.5 Combine like terms: -15.913830463 + -14.5 = -30.413830463 g = -30.413830463 Simplifying g = -30.413830463Solution
The solution to the problem is based on the solutions from the subproblems. g = {1.413830463, -30.413830463}
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