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Simplifying 2(11g2 + 380g + -3595) = 0 Reorder the terms: 2(-3595 + 380g + 11g2) = 0 (-3595 * 2 + 380g * 2 + 11g2 * 2) = 0 (-7190 + 760g + 22g2) = 0 Solving -7190 + 760g + 22g2 = 0 Solving for variable 'g'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3595 + 380g + 11g2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3595 + 380g + 11g2)' equal to zero and attempt to solve: Simplifying -3595 + 380g + 11g2 = 0 Solving -3595 + 380g + 11g2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -326.8181818 + 34.54545455g + g2 = 0 Move the constant term to the right: Add '326.8181818' to each side of the equation. -326.8181818 + 34.54545455g + 326.8181818 + g2 = 0 + 326.8181818 Reorder the terms: -326.8181818 + 326.8181818 + 34.54545455g + g2 = 0 + 326.8181818 Combine like terms: -326.8181818 + 326.8181818 = 0.0000000 0.0000000 + 34.54545455g + g2 = 0 + 326.8181818 34.54545455g + g2 = 0 + 326.8181818 Combine like terms: 0 + 326.8181818 = 326.8181818 34.54545455g + g2 = 326.8181818 The g term is 34.54545455g. Take half its coefficient (17.27272728). Square it (298.3471077) and add it to both sides. Add '298.3471077' to each side of the equation. 34.54545455g + 298.3471077 + g2 = 326.8181818 + 298.3471077 Reorder the terms: 298.3471077 + 34.54545455g + g2 = 326.8181818 + 298.3471077 Combine like terms: 326.8181818 + 298.3471077 = 625.1652895 298.3471077 + 34.54545455g + g2 = 625.1652895 Factor a perfect square on the left side: (g + 17.27272728)(g + 17.27272728) = 625.1652895 Calculate the square root of the right side: 25.003305571 Break this problem into two subproblems by setting (g + 17.27272728) equal to 25.003305571 and -25.003305571.Subproblem 1
g + 17.27272728 = 25.003305571 Simplifying g + 17.27272728 = 25.003305571 Reorder the terms: 17.27272728 + g = 25.003305571 Solving 17.27272728 + g = 25.003305571 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-17.27272728' to each side of the equation. 17.27272728 + -17.27272728 + g = 25.003305571 + -17.27272728 Combine like terms: 17.27272728 + -17.27272728 = 0.00000000 0.00000000 + g = 25.003305571 + -17.27272728 g = 25.003305571 + -17.27272728 Combine like terms: 25.003305571 + -17.27272728 = 7.730578291 g = 7.730578291 Simplifying g = 7.730578291Subproblem 2
g + 17.27272728 = -25.003305571 Simplifying g + 17.27272728 = -25.003305571 Reorder the terms: 17.27272728 + g = -25.003305571 Solving 17.27272728 + g = -25.003305571 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-17.27272728' to each side of the equation. 17.27272728 + -17.27272728 + g = -25.003305571 + -17.27272728 Combine like terms: 17.27272728 + -17.27272728 = 0.00000000 0.00000000 + g = -25.003305571 + -17.27272728 g = -25.003305571 + -17.27272728 Combine like terms: -25.003305571 + -17.27272728 = -42.276032851 g = -42.276032851 Simplifying g = -42.276032851Solution
The solution to the problem is based on the solutions from the subproblems. g = {7.730578291, -42.276032851}Solution
g = {7.730578291, -42.276032851}
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