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Simplifying 12g2 + -36g + -2 = -13 Reorder the terms: -2 + -36g + 12g2 = -13 Solving -2 + -36g + 12g2 = -13 Solving for variable 'g'. Reorder the terms: -2 + 13 + -36g + 12g2 = -13 + 13 Combine like terms: -2 + 13 = 11 11 + -36g + 12g2 = -13 + 13 Combine like terms: -13 + 13 = 0 11 + -36g + 12g2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.9166666667 + -3g + g2 = 0 Move the constant term to the right: Add '-0.9166666667' to each side of the equation. 0.9166666667 + -3g + -0.9166666667 + g2 = 0 + -0.9166666667 Reorder the terms: 0.9166666667 + -0.9166666667 + -3g + g2 = 0 + -0.9166666667 Combine like terms: 0.9166666667 + -0.9166666667 = 0.0000000000 0.0000000000 + -3g + g2 = 0 + -0.9166666667 -3g + g2 = 0 + -0.9166666667 Combine like terms: 0 + -0.9166666667 = -0.9166666667 -3g + g2 = -0.9166666667 The g term is -3g. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3g + 2.25 + g2 = -0.9166666667 + 2.25 Reorder the terms: 2.25 + -3g + g2 = -0.9166666667 + 2.25 Combine like terms: -0.9166666667 + 2.25 = 1.3333333333 2.25 + -3g + g2 = 1.3333333333 Factor a perfect square on the left side: (g + -1.5)(g + -1.5) = 1.3333333333 Calculate the square root of the right side: 1.154700538 Break this problem into two subproblems by setting (g + -1.5) equal to 1.154700538 and -1.154700538.Subproblem 1
g + -1.5 = 1.154700538 Simplifying g + -1.5 = 1.154700538 Reorder the terms: -1.5 + g = 1.154700538 Solving -1.5 + g = 1.154700538 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + g = 1.154700538 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + g = 1.154700538 + 1.5 g = 1.154700538 + 1.5 Combine like terms: 1.154700538 + 1.5 = 2.654700538 g = 2.654700538 Simplifying g = 2.654700538Subproblem 2
g + -1.5 = -1.154700538 Simplifying g + -1.5 = -1.154700538 Reorder the terms: -1.5 + g = -1.154700538 Solving -1.5 + g = -1.154700538 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + g = -1.154700538 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + g = -1.154700538 + 1.5 g = -1.154700538 + 1.5 Combine like terms: -1.154700538 + 1.5 = 0.345299462 g = 0.345299462 Simplifying g = 0.345299462Solution
The solution to the problem is based on the solutions from the subproblems. g = {2.654700538, 0.345299462}
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