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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 = 4 4 + -13g + 4g2 = -6 + 6 Combine like terms: -6 + 6 = 0 4 + -13g + 4g2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1 + -3.25g + g2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -3.25g + -1 + g2 = 0 + -1 Reorder the terms: 1 + -1 + -3.25g + g2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3.25g + g2 = 0 + -1 -3.25g + g2 = 0 + -1 Combine like terms: 0 + -1 = -1 -3.25g + g2 = -1 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 = -1 + 2.640625 Reorder the terms: 2.640625 + -3.25g + g2 = -1 + 2.640625 Combine like terms: -1 + 2.640625 = 1.640625 2.640625 + -3.25g + g2 = 1.640625 Factor a perfect square on the left side: (g + -1.625)(g + -1.625) = 1.640625 Calculate the square root of the right side: 1.280868846 Break this problem into two subproblems by setting (g + -1.625) equal to 1.280868846 and -1.280868846.Subproblem 1
g + -1.625 = 1.280868846 Simplifying g + -1.625 = 1.280868846 Reorder the terms: -1.625 + g = 1.280868846 Solving -1.625 + g = 1.280868846 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 = 1.280868846 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + g = 1.280868846 + 1.625 g = 1.280868846 + 1.625 Combine like terms: 1.280868846 + 1.625 = 2.905868846 g = 2.905868846 Simplifying g = 2.905868846Subproblem 2
g + -1.625 = -1.280868846 Simplifying g + -1.625 = -1.280868846 Reorder the terms: -1.625 + g = -1.280868846 Solving -1.625 + g = -1.280868846 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 = -1.280868846 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + g = -1.280868846 + 1.625 g = -1.280868846 + 1.625 Combine like terms: -1.280868846 + 1.625 = 0.344131154 g = 0.344131154 Simplifying g = 0.344131154Solution
The solution to the problem is based on the solutions from the subproblems. g = {2.905868846, 0.344131154}
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