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Simplifying 7g3 + 21g2 + -14g = 0 Reorder the terms: -14g + 21g2 + 7g3 = 0 Solving -14g + 21g2 + 7g3 = 0 Solving for variable 'g'. Factor out the Greatest Common Factor (GCF), '7g'. 7g(-2 + 3g + g2) = 0 Ignore the factor 7.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 '(-2 + 3g + g2)' equal to zero and attempt to solve: Simplifying -2 + 3g + g2 = 0 Solving -2 + 3g + g2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 3g + 2 + g2 = 0 + 2 Reorder the terms: -2 + 2 + 3g + g2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3g + g2 = 0 + 2 3g + g2 = 0 + 2 Combine like terms: 0 + 2 = 2 3g + g2 = 2 The g term is 3g. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3g + 2.25 + g2 = 2 + 2.25 Reorder the terms: 2.25 + 3g + g2 = 2 + 2.25 Combine like terms: 2 + 2.25 = 4.25 2.25 + 3g + g2 = 4.25 Factor a perfect square on the left side: (g + 1.5)(g + 1.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (g + 1.5) equal to 2.061552813 and -2.061552813.Subproblem 1
g + 1.5 = 2.061552813 Simplifying g + 1.5 = 2.061552813 Reorder the terms: 1.5 + g = 2.061552813 Solving 1.5 + g = 2.061552813 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + g = 2.061552813 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + g = 2.061552813 + -1.5 g = 2.061552813 + -1.5 Combine like terms: 2.061552813 + -1.5 = 0.561552813 g = 0.561552813 Simplifying g = 0.561552813Subproblem 2
g + 1.5 = -2.061552813 Simplifying g + 1.5 = -2.061552813 Reorder the terms: 1.5 + g = -2.061552813 Solving 1.5 + g = -2.061552813 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + g = -2.061552813 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + g = -2.061552813 + -1.5 g = -2.061552813 + -1.5 Combine like terms: -2.061552813 + -1.5 = -3.561552813 g = -3.561552813 Simplifying g = -3.561552813Solution
The solution to the problem is based on the solutions from the subproblems. g = {0.561552813, -3.561552813}Solution
g = {0, 0.561552813, -3.561552813}
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