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Simplifying -3g + -2 + -1(-4g + 10) * g = 6 Reorder the terms: -3g + -2 + -1(10 + -4g) * g = 6 Reorder the terms for easier multiplication: -3g + -2 + -1g(10 + -4g) = 6 -3g + -2 + (10 * -1g + -4g * -1g) = 6 -3g + -2 + (-10g + 4g2) = 6 Reorder the terms: -2 + -3g + -10g + 4g2 = 6 Combine like terms: -3g + -10g = -13g -2 + -13g + 4g2 = 6 Solving -2 + -13g + 4g2 = 6 Solving for variable 'g'. Reorder the terms: -2 + -6 + -13g + 4g2 = 6 + -6 Combine like terms: -2 + -6 = -8 -8 + -13g + 4g2 = 6 + -6 Combine like terms: 6 + -6 = 0 -8 + -13g + 4g2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2 + -3.25g + g2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -3.25g + 2 + g2 = 0 + 2 Reorder the terms: -2 + 2 + -3.25g + g2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3.25g + g2 = 0 + 2 -3.25g + g2 = 0 + 2 Combine like terms: 0 + 2 = 2 -3.25g + g2 = 2 The g term is -3.25g. Take half its coefficient (-1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. -3.25g + 2.640625 + g2 = 2 + 2.640625 Reorder the terms: 2.640625 + -3.25g + g2 = 2 + 2.640625 Combine like terms: 2 + 2.640625 = 4.640625 2.640625 + -3.25g + g2 = 4.640625 Factor a perfect square on the left side: (g + -1.625)(g + -1.625) = 4.640625 Calculate the square root of the right side: 2.154210992 Break this problem into two subproblems by setting (g + -1.625) equal to 2.154210992 and -2.154210992.Subproblem 1
g + -1.625 = 2.154210992 Simplifying g + -1.625 = 2.154210992 Reorder the terms: -1.625 + g = 2.154210992 Solving -1.625 + g = 2.154210992 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + g = 2.154210992 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + g = 2.154210992 + 1.625 g = 2.154210992 + 1.625 Combine like terms: 2.154210992 + 1.625 = 3.779210992 g = 3.779210992 Simplifying g = 3.779210992Subproblem 2
g + -1.625 = -2.154210992 Simplifying g + -1.625 = -2.154210992 Reorder the terms: -1.625 + g = -2.154210992 Solving -1.625 + g = -2.154210992 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + g = -2.154210992 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + g = -2.154210992 + 1.625 g = -2.154210992 + 1.625 Combine like terms: -2.154210992 + 1.625 = -0.529210992 g = -0.529210992 Simplifying g = -0.529210992Solution
The solution to the problem is based on the solutions from the subproblems. g = {3.779210992, -0.529210992}
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