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Simplifying 48g2 + 1 = -18g Reorder the terms: 1 + 48g2 = -18g Solving 1 + 48g2 = -18g Solving for variable 'g'. Reorder the terms: 1 + 18g + 48g2 = -18g + 18g Combine like terms: -18g + 18g = 0 1 + 18g + 48g2 = 0 Begin completing the square. Divide all terms by 48 the coefficient of the squared term: Divide each side by '48'. 0.02083333333 + 0.375g + g2 = 0 Move the constant term to the right: Add '-0.02083333333' to each side of the equation. 0.02083333333 + 0.375g + -0.02083333333 + g2 = 0 + -0.02083333333 Reorder the terms: 0.02083333333 + -0.02083333333 + 0.375g + g2 = 0 + -0.02083333333 Combine like terms: 0.02083333333 + -0.02083333333 = 0.00000000000 0.00000000000 + 0.375g + g2 = 0 + -0.02083333333 0.375g + g2 = 0 + -0.02083333333 Combine like terms: 0 + -0.02083333333 = -0.02083333333 0.375g + g2 = -0.02083333333 The g term is 0.375g. Take half its coefficient (0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. 0.375g + 0.03515625 + g2 = -0.02083333333 + 0.03515625 Reorder the terms: 0.03515625 + 0.375g + g2 = -0.02083333333 + 0.03515625 Combine like terms: -0.02083333333 + 0.03515625 = 0.01432291667 0.03515625 + 0.375g + g2 = 0.01432291667 Factor a perfect square on the left side: (g + 0.1875)(g + 0.1875) = 0.01432291667 Calculate the square root of the right side: 0.119678388 Break this problem into two subproblems by setting (g + 0.1875) equal to 0.119678388 and -0.119678388.Subproblem 1
g + 0.1875 = 0.119678388 Simplifying g + 0.1875 = 0.119678388 Reorder the terms: 0.1875 + g = 0.119678388 Solving 0.1875 + g = 0.119678388 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + g = 0.119678388 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + g = 0.119678388 + -0.1875 g = 0.119678388 + -0.1875 Combine like terms: 0.119678388 + -0.1875 = -0.067821612 g = -0.067821612 Simplifying g = -0.067821612Subproblem 2
g + 0.1875 = -0.119678388 Simplifying g + 0.1875 = -0.119678388 Reorder the terms: 0.1875 + g = -0.119678388 Solving 0.1875 + g = -0.119678388 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + g = -0.119678388 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + g = -0.119678388 + -0.1875 g = -0.119678388 + -0.1875 Combine like terms: -0.119678388 + -0.1875 = -0.307178388 g = -0.307178388 Simplifying g = -0.307178388Solution
The solution to the problem is based on the solutions from the subproblems. g = {-0.067821612, -0.307178388}
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