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Simplifying 3g2 + -12g = 4 Reorder the terms: -12g + 3g2 = 4 Solving -12g + 3g2 = 4 Solving for variable 'g'. Reorder the terms: -4 + -12g + 3g2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + -12g + 3g2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.333333333 + -4g + g2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + -4g + 1.333333333 + g2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + -4g + g2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + -4g + g2 = 0 + 1.333333333 -4g + g2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 -4g + g2 = 1.333333333 The g term is -4g. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4g + 4 + g2 = 1.333333333 + 4 Reorder the terms: 4 + -4g + g2 = 1.333333333 + 4 Combine like terms: 1.333333333 + 4 = 5.333333333 4 + -4g + g2 = 5.333333333 Factor a perfect square on the left side: (g + -2)(g + -2) = 5.333333333 Calculate the square root of the right side: 2.309401077 Break this problem into two subproblems by setting (g + -2) equal to 2.309401077 and -2.309401077.Subproblem 1
g + -2 = 2.309401077 Simplifying g + -2 = 2.309401077 Reorder the terms: -2 + g = 2.309401077 Solving -2 + g = 2.309401077 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + g = 2.309401077 + 2 Combine like terms: -2 + 2 = 0 0 + g = 2.309401077 + 2 g = 2.309401077 + 2 Combine like terms: 2.309401077 + 2 = 4.309401077 g = 4.309401077 Simplifying g = 4.309401077Subproblem 2
g + -2 = -2.309401077 Simplifying g + -2 = -2.309401077 Reorder the terms: -2 + g = -2.309401077 Solving -2 + g = -2.309401077 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + g = -2.309401077 + 2 Combine like terms: -2 + 2 = 0 0 + g = -2.309401077 + 2 g = -2.309401077 + 2 Combine like terms: -2.309401077 + 2 = -0.309401077 g = -0.309401077 Simplifying g = -0.309401077Solution
The solution to the problem is based on the solutions from the subproblems. g = {4.309401077, -0.309401077}
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