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Simplifying 1.7g(g + -0.5) + -6.4(-1g + 2) = 0 Reorder the terms: 1.7g(-0.5 + g) + -6.4(-1g + 2) = 0 (-0.5 * 1.7g + g * 1.7g) + -6.4(-1g + 2) = 0 (-0.85g + 1.7g2) + -6.4(-1g + 2) = 0 Reorder the terms: -0.85g + 1.7g2 + -6.4(2 + -1g) = 0 -0.85g + 1.7g2 + (2 * -6.4 + -1g * -6.4) = 0 -0.85g + 1.7g2 + (-12.8 + 6.4g) = 0 Reorder the terms: -12.8 + -0.85g + 6.4g + 1.7g2 = 0 Combine like terms: -0.85g + 6.4g = 5.55g -12.8 + 5.55g + 1.7g2 = 0 Solving -12.8 + 5.55g + 1.7g2 = 0 Solving for variable 'g'. Begin completing the square. Divide all terms by 1.7 the coefficient of the squared term: Divide each side by '1.7'. -7.529411765 + 3.264705882g + g2 = 0 Move the constant term to the right: Add '7.529411765' to each side of the equation. -7.529411765 + 3.264705882g + 7.529411765 + g2 = 0 + 7.529411765 Reorder the terms: -7.529411765 + 7.529411765 + 3.264705882g + g2 = 0 + 7.529411765 Combine like terms: -7.529411765 + 7.529411765 = 0.000000000 0.000000000 + 3.264705882g + g2 = 0 + 7.529411765 3.264705882g + g2 = 0 + 7.529411765 Combine like terms: 0 + 7.529411765 = 7.529411765 3.264705882g + g2 = 7.529411765 The g term is 3.264705882g. Take half its coefficient (1.632352941). Square it (2.664576124) and add it to both sides. Add '2.664576124' to each side of the equation. 3.264705882g + 2.664576124 + g2 = 7.529411765 + 2.664576124 Reorder the terms: 2.664576124 + 3.264705882g + g2 = 7.529411765 + 2.664576124 Combine like terms: 7.529411765 + 2.664576124 = 10.193987889 2.664576124 + 3.264705882g + g2 = 10.193987889 Factor a perfect square on the left side: (g + 1.632352941)(g + 1.632352941) = 10.193987889 Calculate the square root of the right side: 3.192802513 Break this problem into two subproblems by setting (g + 1.632352941) equal to 3.192802513 and -3.192802513.Subproblem 1
g + 1.632352941 = 3.192802513 Simplifying g + 1.632352941 = 3.192802513 Reorder the terms: 1.632352941 + g = 3.192802513 Solving 1.632352941 + g = 3.192802513 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-1.632352941' to each side of the equation. 1.632352941 + -1.632352941 + g = 3.192802513 + -1.632352941 Combine like terms: 1.632352941 + -1.632352941 = 0.000000000 0.000000000 + g = 3.192802513 + -1.632352941 g = 3.192802513 + -1.632352941 Combine like terms: 3.192802513 + -1.632352941 = 1.560449572 g = 1.560449572 Simplifying g = 1.560449572Subproblem 2
g + 1.632352941 = -3.192802513 Simplifying g + 1.632352941 = -3.192802513 Reorder the terms: 1.632352941 + g = -3.192802513 Solving 1.632352941 + g = -3.192802513 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-1.632352941' to each side of the equation. 1.632352941 + -1.632352941 + g = -3.192802513 + -1.632352941 Combine like terms: 1.632352941 + -1.632352941 = 0.000000000 0.000000000 + g = -3.192802513 + -1.632352941 g = -3.192802513 + -1.632352941 Combine like terms: -3.192802513 + -1.632352941 = -4.825155454 g = -4.825155454 Simplifying g = -4.825155454Solution
The solution to the problem is based on the solutions from the subproblems. g = {1.560449572, -4.825155454}
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