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Simplifying g2 + -19g = 44 Reorder the terms: -19g + g2 = 44 Solving -19g + g2 = 44 Solving for variable 'g'. Reorder the terms: -44 + -19g + g2 = 44 + -44 Combine like terms: 44 + -44 = 0 -44 + -19g + g2 = 0 Begin completing the square. Move the constant term to the right: Add '44' to each side of the equation. -44 + -19g + 44 + g2 = 0 + 44 Reorder the terms: -44 + 44 + -19g + g2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + -19g + g2 = 0 + 44 -19g + g2 = 0 + 44 Combine like terms: 0 + 44 = 44 -19g + g2 = 44 The g term is -19g. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19g + 90.25 + g2 = 44 + 90.25 Reorder the terms: 90.25 + -19g + g2 = 44 + 90.25 Combine like terms: 44 + 90.25 = 134.25 90.25 + -19g + g2 = 134.25 Factor a perfect square on the left side: (g + -9.5)(g + -9.5) = 134.25 Calculate the square root of the right side: 11.586630226 Break this problem into two subproblems by setting (g + -9.5) equal to 11.586630226 and -11.586630226.Subproblem 1
g + -9.5 = 11.586630226 Simplifying g + -9.5 = 11.586630226 Reorder the terms: -9.5 + g = 11.586630226 Solving -9.5 + g = 11.586630226 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + g = 11.586630226 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + g = 11.586630226 + 9.5 g = 11.586630226 + 9.5 Combine like terms: 11.586630226 + 9.5 = 21.086630226 g = 21.086630226 Simplifying g = 21.086630226Subproblem 2
g + -9.5 = -11.586630226 Simplifying g + -9.5 = -11.586630226 Reorder the terms: -9.5 + g = -11.586630226 Solving -9.5 + g = -11.586630226 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + g = -11.586630226 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + g = -11.586630226 + 9.5 g = -11.586630226 + 9.5 Combine like terms: -11.586630226 + 9.5 = -2.086630226 g = -2.086630226 Simplifying g = -2.086630226Solution
The solution to the problem is based on the solutions from the subproblems. g = {21.086630226, -2.086630226}
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