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Simplifying -2g2 + 40g = -6 Reorder the terms: 40g + -2g2 = -6 Solving 40g + -2g2 = -6 Solving for variable 'g'. Reorder the terms: 6 + 40g + -2g2 = -6 + 6 Combine like terms: -6 + 6 = 0 6 + 40g + -2g2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 20g + -1g2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 20g + -1g2)' equal to zero and attempt to solve: Simplifying 3 + 20g + -1g2 = 0 Solving 3 + 20g + -1g2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3 + -20g + g2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -20g + 3 + g2 = 0 + 3 Reorder the terms: -3 + 3 + -20g + g2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -20g + g2 = 0 + 3 -20g + g2 = 0 + 3 Combine like terms: 0 + 3 = 3 -20g + g2 = 3 The g term is -20g. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20g + 100 + g2 = 3 + 100 Reorder the terms: 100 + -20g + g2 = 3 + 100 Combine like terms: 3 + 100 = 103 100 + -20g + g2 = 103 Factor a perfect square on the left side: (g + -10)(g + -10) = 103 Calculate the square root of the right side: 10.148891565 Break this problem into two subproblems by setting (g + -10) equal to 10.148891565 and -10.148891565.Subproblem 1
g + -10 = 10.148891565 Simplifying g + -10 = 10.148891565 Reorder the terms: -10 + g = 10.148891565 Solving -10 + g = 10.148891565 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + g = 10.148891565 + 10 Combine like terms: -10 + 10 = 0 0 + g = 10.148891565 + 10 g = 10.148891565 + 10 Combine like terms: 10.148891565 + 10 = 20.148891565 g = 20.148891565 Simplifying g = 20.148891565Subproblem 2
g + -10 = -10.148891565 Simplifying g + -10 = -10.148891565 Reorder the terms: -10 + g = -10.148891565 Solving -10 + g = -10.148891565 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + g = -10.148891565 + 10 Combine like terms: -10 + 10 = 0 0 + g = -10.148891565 + 10 g = -10.148891565 + 10 Combine like terms: -10.148891565 + 10 = -0.148891565 g = -0.148891565 Simplifying g = -0.148891565Solution
The solution to the problem is based on the solutions from the subproblems. g = {20.148891565, -0.148891565}Solution
g = {20.148891565, -0.148891565}
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