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Simplifying G2 + 4G = 2 Reorder the terms: 4G + G2 = 2 Solving 4G + G2 = 2 Solving for variable 'G'. Reorder the terms: -2 + 4G + G2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 4G + G2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 4G + 2 + G2 = 0 + 2 Reorder the terms: -2 + 2 + 4G + G2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 4G + G2 = 0 + 2 4G + G2 = 0 + 2 Combine like terms: 0 + 2 = 2 4G + G2 = 2 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 = 2 + 4 Reorder the terms: 4 + 4G + G2 = 2 + 4 Combine like terms: 2 + 4 = 6 4 + 4G + G2 = 6 Factor a perfect square on the left side: (G + 2)(G + 2) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (G + 2) equal to 2.449489743 and -2.449489743.Subproblem 1
G + 2 = 2.449489743 Simplifying G + 2 = 2.449489743 Reorder the terms: 2 + G = 2.449489743 Solving 2 + G = 2.449489743 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 = 2.449489743 + -2 Combine like terms: 2 + -2 = 0 0 + G = 2.449489743 + -2 G = 2.449489743 + -2 Combine like terms: 2.449489743 + -2 = 0.449489743 G = 0.449489743 Simplifying G = 0.449489743Subproblem 2
G + 2 = -2.449489743 Simplifying G + 2 = -2.449489743 Reorder the terms: 2 + G = -2.449489743 Solving 2 + G = -2.449489743 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 = -2.449489743 + -2 Combine like terms: 2 + -2 = 0 0 + G = -2.449489743 + -2 G = -2.449489743 + -2 Combine like terms: -2.449489743 + -2 = -4.449489743 G = -4.449489743 Simplifying G = -4.449489743Solution
The solution to the problem is based on the solutions from the subproblems. G = {0.449489743, -4.449489743}
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