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Simplifying g + -3 = -1g2 Reorder the terms: -3 + g = -1g2 Solving -3 + g = -1g2 Solving for variable 'g'. Combine like terms: -1g2 + g2 = 0 -3 + g + g2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + g + 3 + g2 = 0 + 3 Reorder the terms: -3 + 3 + g + g2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + g + g2 = 0 + 3 g + g2 = 0 + 3 Combine like terms: 0 + 3 = 3 g + g2 = 3 The g term is g. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. g + 0.25 + g2 = 3 + 0.25 Reorder the terms: 0.25 + g + g2 = 3 + 0.25 Combine like terms: 3 + 0.25 = 3.25 0.25 + g + g2 = 3.25 Factor a perfect square on the left side: (g + 0.5)(g + 0.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (g + 0.5) equal to 1.802775638 and -1.802775638.Subproblem 1
g + 0.5 = 1.802775638 Simplifying g + 0.5 = 1.802775638 Reorder the terms: 0.5 + g = 1.802775638 Solving 0.5 + g = 1.802775638 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + g = 1.802775638 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + g = 1.802775638 + -0.5 g = 1.802775638 + -0.5 Combine like terms: 1.802775638 + -0.5 = 1.302775638 g = 1.302775638 Simplifying g = 1.302775638Subproblem 2
g + 0.5 = -1.802775638 Simplifying g + 0.5 = -1.802775638 Reorder the terms: 0.5 + g = -1.802775638 Solving 0.5 + g = -1.802775638 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + g = -1.802775638 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + g = -1.802775638 + -0.5 g = -1.802775638 + -0.5 Combine like terms: -1.802775638 + -0.5 = -2.302775638 g = -2.302775638 Simplifying g = -2.302775638Solution
The solution to the problem is based on the solutions from the subproblems. g = {1.302775638, -2.302775638}
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