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Simplifying 2g2 + -44g = -26 Reorder the terms: -44g + 2g2 = -26 Solving -44g + 2g2 = -26 Solving for variable 'g'. Reorder the terms: 26 + -44g + 2g2 = -26 + 26 Combine like terms: -26 + 26 = 0 26 + -44g + 2g2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(13 + -22g + g2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(13 + -22g + g2)' equal to zero and attempt to solve: Simplifying 13 + -22g + g2 = 0 Solving 13 + -22g + g2 = 0 Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + -22g + -13 + g2 = 0 + -13 Reorder the terms: 13 + -13 + -22g + g2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -22g + g2 = 0 + -13 -22g + g2 = 0 + -13 Combine like terms: 0 + -13 = -13 -22g + g2 = -13 The g term is -22g. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22g + 121 + g2 = -13 + 121 Reorder the terms: 121 + -22g + g2 = -13 + 121 Combine like terms: -13 + 121 = 108 121 + -22g + g2 = 108 Factor a perfect square on the left side: (g + -11)(g + -11) = 108 Calculate the square root of the right side: 10.392304845 Break this problem into two subproblems by setting (g + -11) equal to 10.392304845 and -10.392304845.Subproblem 1
g + -11 = 10.392304845 Simplifying g + -11 = 10.392304845 Reorder the terms: -11 + g = 10.392304845 Solving -11 + g = 10.392304845 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + g = 10.392304845 + 11 Combine like terms: -11 + 11 = 0 0 + g = 10.392304845 + 11 g = 10.392304845 + 11 Combine like terms: 10.392304845 + 11 = 21.392304845 g = 21.392304845 Simplifying g = 21.392304845Subproblem 2
g + -11 = -10.392304845 Simplifying g + -11 = -10.392304845 Reorder the terms: -11 + g = -10.392304845 Solving -11 + g = -10.392304845 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + g = -10.392304845 + 11 Combine like terms: -11 + 11 = 0 0 + g = -10.392304845 + 11 g = -10.392304845 + 11 Combine like terms: -10.392304845 + 11 = 0.607695155 g = 0.607695155 Simplifying g = 0.607695155Solution
The solution to the problem is based on the solutions from the subproblems. g = {21.392304845, 0.607695155}Solution
g = {21.392304845, 0.607695155}
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