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Simplifying g2 + 4g + -6 = 0 Reorder the terms: -6 + 4g + g2 = 0 Solving -6 + 4g + g2 = 0 Solving for variable 'g'. Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 4g + 6 + g2 = 0 + 6 Reorder the terms: -6 + 6 + 4g + g2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 4g + g2 = 0 + 6 4g + g2 = 0 + 6 Combine like terms: 0 + 6 = 6 4g + g2 = 6 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 = 6 + 4 Reorder the terms: 4 + 4g + g2 = 6 + 4 Combine like terms: 6 + 4 = 10 4 + 4g + g2 = 10 Factor a perfect square on the left side: (g + 2)(g + 2) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (g + 2) equal to 3.16227766 and -3.16227766.Subproblem 1
g + 2 = 3.16227766 Simplifying g + 2 = 3.16227766 Reorder the terms: 2 + g = 3.16227766 Solving 2 + g = 3.16227766 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 = 3.16227766 + -2 Combine like terms: 2 + -2 = 0 0 + g = 3.16227766 + -2 g = 3.16227766 + -2 Combine like terms: 3.16227766 + -2 = 1.16227766 g = 1.16227766 Simplifying g = 1.16227766Subproblem 2
g + 2 = -3.16227766 Simplifying g + 2 = -3.16227766 Reorder the terms: 2 + g = -3.16227766 Solving 2 + g = -3.16227766 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 = -3.16227766 + -2 Combine like terms: 2 + -2 = 0 0 + g = -3.16227766 + -2 g = -3.16227766 + -2 Combine like terms: -3.16227766 + -2 = -5.16227766 g = -5.16227766 Simplifying g = -5.16227766Solution
The solution to the problem is based on the solutions from the subproblems. g = {1.16227766, -5.16227766}
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