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Simplifying 7g2 + -3g + -3 = 0 Reorder the terms: -3 + -3g + 7g2 = 0 Solving -3 + -3g + 7g2 = 0 Solving for variable 'g'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.4285714286 + -0.4285714286g + g2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + -0.4285714286g + 0.4285714286 + g2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + -0.4285714286g + g2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + -0.4285714286g + g2 = 0 + 0.4285714286 -0.4285714286g + g2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 -0.4285714286g + g2 = 0.4285714286 The g term is -0.4285714286g. Take half its coefficient (-0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. -0.4285714286g + 0.04591836735 + g2 = 0.4285714286 + 0.04591836735 Reorder the terms: 0.04591836735 + -0.4285714286g + g2 = 0.4285714286 + 0.04591836735 Combine like terms: 0.4285714286 + 0.04591836735 = 0.47448979595 0.04591836735 + -0.4285714286g + g2 = 0.47448979595 Factor a perfect square on the left side: (g + -0.2142857143)(g + -0.2142857143) = 0.47448979595 Calculate the square root of the right side: 0.688832197 Break this problem into two subproblems by setting (g + -0.2142857143) equal to 0.688832197 and -0.688832197.Subproblem 1
g + -0.2142857143 = 0.688832197 Simplifying g + -0.2142857143 = 0.688832197 Reorder the terms: -0.2142857143 + g = 0.688832197 Solving -0.2142857143 + g = 0.688832197 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + g = 0.688832197 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + g = 0.688832197 + 0.2142857143 g = 0.688832197 + 0.2142857143 Combine like terms: 0.688832197 + 0.2142857143 = 0.9031179113 g = 0.9031179113 Simplifying g = 0.9031179113Subproblem 2
g + -0.2142857143 = -0.688832197 Simplifying g + -0.2142857143 = -0.688832197 Reorder the terms: -0.2142857143 + g = -0.688832197 Solving -0.2142857143 + g = -0.688832197 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + g = -0.688832197 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + g = -0.688832197 + 0.2142857143 g = -0.688832197 + 0.2142857143 Combine like terms: -0.688832197 + 0.2142857143 = -0.4745464827 g = -0.4745464827 Simplifying g = -0.4745464827Solution
The solution to the problem is based on the solutions from the subproblems. g = {0.9031179113, -0.4745464827}
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