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Simplifying g2 + -6g = 35 Reorder the terms: -6g + g2 = 35 Solving -6g + g2 = 35 Solving for variable 'g'. Reorder the terms: -35 + -6g + g2 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + -6g + g2 = 0 Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + -6g + 35 + g2 = 0 + 35 Reorder the terms: -35 + 35 + -6g + g2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -6g + g2 = 0 + 35 -6g + g2 = 0 + 35 Combine like terms: 0 + 35 = 35 -6g + g2 = 35 The g term is -6g. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6g + 9 + g2 = 35 + 9 Reorder the terms: 9 + -6g + g2 = 35 + 9 Combine like terms: 35 + 9 = 44 9 + -6g + g2 = 44 Factor a perfect square on the left side: (g + -3)(g + -3) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (g + -3) equal to 6.633249581 and -6.633249581.Subproblem 1
g + -3 = 6.633249581 Simplifying g + -3 = 6.633249581 Reorder the terms: -3 + g = 6.633249581 Solving -3 + g = 6.633249581 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + g = 6.633249581 + 3 Combine like terms: -3 + 3 = 0 0 + g = 6.633249581 + 3 g = 6.633249581 + 3 Combine like terms: 6.633249581 + 3 = 9.633249581 g = 9.633249581 Simplifying g = 9.633249581Subproblem 2
g + -3 = -6.633249581 Simplifying g + -3 = -6.633249581 Reorder the terms: -3 + g = -6.633249581 Solving -3 + g = -6.633249581 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + g = -6.633249581 + 3 Combine like terms: -3 + 3 = 0 0 + g = -6.633249581 + 3 g = -6.633249581 + 3 Combine like terms: -6.633249581 + 3 = -3.633249581 g = -3.633249581 Simplifying g = -3.633249581Solution
The solution to the problem is based on the solutions from the subproblems. g = {9.633249581, -3.633249581}
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