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Simplifying 100g2 + 249g + 144 = 0 Reorder the terms: 144 + 249g + 100g2 = 0 Solving 144 + 249g + 100g2 = 0 Solving for variable 'g'. Begin completing the square. Divide all terms by 100 the coefficient of the squared term: Divide each side by '100'. 1.44 + 2.49g + g2 = 0 Move the constant term to the right: Add '-1.44' to each side of the equation. 1.44 + 2.49g + -1.44 + g2 = 0 + -1.44 Reorder the terms: 1.44 + -1.44 + 2.49g + g2 = 0 + -1.44 Combine like terms: 1.44 + -1.44 = 0.00 0.00 + 2.49g + g2 = 0 + -1.44 2.49g + g2 = 0 + -1.44 Combine like terms: 0 + -1.44 = -1.44 2.49g + g2 = -1.44 The g term is 2.49g. Take half its coefficient (1.245). Square it (1.550025) and add it to both sides. Add '1.550025' to each side of the equation. 2.49g + 1.550025 + g2 = -1.44 + 1.550025 Reorder the terms: 1.550025 + 2.49g + g2 = -1.44 + 1.550025 Combine like terms: -1.44 + 1.550025 = 0.110025 1.550025 + 2.49g + g2 = 0.110025 Factor a perfect square on the left side: (g + 1.245)(g + 1.245) = 0.110025 Calculate the square root of the right side: 0.331700166 Break this problem into two subproblems by setting (g + 1.245) equal to 0.331700166 and -0.331700166.Subproblem 1
g + 1.245 = 0.331700166 Simplifying g + 1.245 = 0.331700166 Reorder the terms: 1.245 + g = 0.331700166 Solving 1.245 + g = 0.331700166 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-1.245' to each side of the equation. 1.245 + -1.245 + g = 0.331700166 + -1.245 Combine like terms: 1.245 + -1.245 = 0.000 0.000 + g = 0.331700166 + -1.245 g = 0.331700166 + -1.245 Combine like terms: 0.331700166 + -1.245 = -0.913299834 g = -0.913299834 Simplifying g = -0.913299834Subproblem 2
g + 1.245 = -0.331700166 Simplifying g + 1.245 = -0.331700166 Reorder the terms: 1.245 + g = -0.331700166 Solving 1.245 + g = -0.331700166 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-1.245' to each side of the equation. 1.245 + -1.245 + g = -0.331700166 + -1.245 Combine like terms: 1.245 + -1.245 = 0.000 0.000 + g = -0.331700166 + -1.245 g = -0.331700166 + -1.245 Combine like terms: -0.331700166 + -1.245 = -1.576700166 g = -1.576700166 Simplifying g = -1.576700166Solution
The solution to the problem is based on the solutions from the subproblems. g = {-0.913299834, -1.576700166}
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