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Simplifying g2 + 4g = 11 Reorder the terms: 4g + g2 = 11 Solving 4g + g2 = 11 Solving for variable 'g'. Reorder the terms: -11 + 4g + g2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + 4g + g2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 4g + 11 + g2 = 0 + 11 Reorder the terms: -11 + 11 + 4g + g2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 4g + g2 = 0 + 11 4g + g2 = 0 + 11 Combine like terms: 0 + 11 = 11 4g + g2 = 11 The g term is 4g. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4g + 4 + g2 = 11 + 4 Reorder the terms: 4 + 4g + g2 = 11 + 4 Combine like terms: 11 + 4 = 15 4 + 4g + g2 = 15 Factor a perfect square on the left side: (g + 2)(g + 2) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (g + 2) equal to 3.872983346 and -3.872983346.Subproblem 1
g + 2 = 3.872983346 Simplifying g + 2 = 3.872983346 Reorder the terms: 2 + g = 3.872983346 Solving 2 + g = 3.872983346 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + g = 3.872983346 + -2 Combine like terms: 2 + -2 = 0 0 + g = 3.872983346 + -2 g = 3.872983346 + -2 Combine like terms: 3.872983346 + -2 = 1.872983346 g = 1.872983346 Simplifying g = 1.872983346Subproblem 2
g + 2 = -3.872983346 Simplifying g + 2 = -3.872983346 Reorder the terms: 2 + g = -3.872983346 Solving 2 + g = -3.872983346 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + g = -3.872983346 + -2 Combine like terms: 2 + -2 = 0 0 + g = -3.872983346 + -2 g = -3.872983346 + -2 Combine like terms: -3.872983346 + -2 = -5.872983346 g = -5.872983346 Simplifying g = -5.872983346Solution
The solution to the problem is based on the solutions from the subproblems. g = {1.872983346, -5.872983346}
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