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Simplifying 8g2 + -7g + -6 = 0 Reorder the terms: -6 + -7g + 8g2 = 0 Solving -6 + -7g + 8g2 = 0 Solving for variable 'g'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.75 + -0.875g + g2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -0.875g + 0.75 + g2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -0.875g + g2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -0.875g + g2 = 0 + 0.75 -0.875g + g2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -0.875g + g2 = 0.75 The g term is -0.875g. Take half its coefficient (-0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. -0.875g + 0.19140625 + g2 = 0.75 + 0.19140625 Reorder the terms: 0.19140625 + -0.875g + g2 = 0.75 + 0.19140625 Combine like terms: 0.75 + 0.19140625 = 0.94140625 0.19140625 + -0.875g + g2 = 0.94140625 Factor a perfect square on the left side: (g + -0.4375)(g + -0.4375) = 0.94140625 Calculate the square root of the right side: 0.970260919 Break this problem into two subproblems by setting (g + -0.4375) equal to 0.970260919 and -0.970260919.Subproblem 1
g + -0.4375 = 0.970260919 Simplifying g + -0.4375 = 0.970260919 Reorder the terms: -0.4375 + g = 0.970260919 Solving -0.4375 + g = 0.970260919 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + g = 0.970260919 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + g = 0.970260919 + 0.4375 g = 0.970260919 + 0.4375 Combine like terms: 0.970260919 + 0.4375 = 1.407760919 g = 1.407760919 Simplifying g = 1.407760919Subproblem 2
g + -0.4375 = -0.970260919 Simplifying g + -0.4375 = -0.970260919 Reorder the terms: -0.4375 + g = -0.970260919 Solving -0.4375 + g = -0.970260919 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + g = -0.970260919 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + g = -0.970260919 + 0.4375 g = -0.970260919 + 0.4375 Combine like terms: -0.970260919 + 0.4375 = -0.532760919 g = -0.532760919 Simplifying g = -0.532760919Solution
The solution to the problem is based on the solutions from the subproblems. g = {1.407760919, -0.532760919}
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