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Simplifying 5g(3g + 7g2 + -9) = 0 Reorder the terms: 5g(-9 + 3g + 7g2) = 0 (-9 * 5g + 3g * 5g + 7g2 * 5g) = 0 (-45g + 15g2 + 35g3) = 0 Solving -45g + 15g2 + 35g3 = 0 Solving for variable 'g'. Factor out the Greatest Common Factor (GCF), '5g'. 5g(-9 + 3g + 7g2) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'g' equal to zero and attempt to solve: Simplifying g = 0 Solving g = 0 Move all terms containing g to the left, all other terms to the right. Simplifying g = 0Subproblem 2
Set the factor '(-9 + 3g + 7g2)' equal to zero and attempt to solve: Simplifying -9 + 3g + 7g2 = 0 Solving -9 + 3g + 7g2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.285714286 + 0.4285714286g + g2 = 0 Move the constant term to the right: Add '1.285714286' to each side of the equation. -1.285714286 + 0.4285714286g + 1.285714286 + g2 = 0 + 1.285714286 Reorder the terms: -1.285714286 + 1.285714286 + 0.4285714286g + g2 = 0 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + 0.4285714286g + g2 = 0 + 1.285714286 0.4285714286g + g2 = 0 + 1.285714286 Combine like terms: 0 + 1.285714286 = 1.285714286 0.4285714286g + g2 = 1.285714286 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 = 1.285714286 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286g + g2 = 1.285714286 + 0.04591836735 Combine like terms: 1.285714286 + 0.04591836735 = 1.33163265335 0.04591836735 + 0.4285714286g + g2 = 1.33163265335 Factor a perfect square on the left side: (g + 0.2142857143)(g + 0.2142857143) = 1.33163265335 Calculate the square root of the right side: 1.153963887 Break this problem into two subproblems by setting (g + 0.2142857143) equal to 1.153963887 and -1.153963887.Subproblem 1
g + 0.2142857143 = 1.153963887 Simplifying g + 0.2142857143 = 1.153963887 Reorder the terms: 0.2142857143 + g = 1.153963887 Solving 0.2142857143 + g = 1.153963887 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 = 1.153963887 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + g = 1.153963887 + -0.2142857143 g = 1.153963887 + -0.2142857143 Combine like terms: 1.153963887 + -0.2142857143 = 0.9396781727 g = 0.9396781727 Simplifying g = 0.9396781727Subproblem 2
g + 0.2142857143 = -1.153963887 Simplifying g + 0.2142857143 = -1.153963887 Reorder the terms: 0.2142857143 + g = -1.153963887 Solving 0.2142857143 + g = -1.153963887 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 = -1.153963887 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + g = -1.153963887 + -0.2142857143 g = -1.153963887 + -0.2142857143 Combine like terms: -1.153963887 + -0.2142857143 = -1.3682496013 g = -1.3682496013 Simplifying g = -1.3682496013Solution
The solution to the problem is based on the solutions from the subproblems. g = {0.9396781727, -1.3682496013}Solution
g = {0, 0.9396781727, -1.3682496013}
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