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Simplifying g2 + -2g + -6 = 0 Reorder the terms: -6 + -2g + g2 = 0 Solving -6 + -2g + 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 + -2g + 6 + g2 = 0 + 6 Reorder the terms: -6 + 6 + -2g + g2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -2g + g2 = 0 + 6 -2g + g2 = 0 + 6 Combine like terms: 0 + 6 = 6 -2g + g2 = 6 The g term is -2g. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2g + 1 + g2 = 6 + 1 Reorder the terms: 1 + -2g + g2 = 6 + 1 Combine like terms: 6 + 1 = 7 1 + -2g + g2 = 7 Factor a perfect square on the left side: (g + -1)(g + -1) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (g + -1) equal to 2.645751311 and -2.645751311.Subproblem 1
g + -1 = 2.645751311 Simplifying g + -1 = 2.645751311 Reorder the terms: -1 + g = 2.645751311 Solving -1 + g = 2.645751311 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + g = 2.645751311 + 1 Combine like terms: -1 + 1 = 0 0 + g = 2.645751311 + 1 g = 2.645751311 + 1 Combine like terms: 2.645751311 + 1 = 3.645751311 g = 3.645751311 Simplifying g = 3.645751311Subproblem 2
g + -1 = -2.645751311 Simplifying g + -1 = -2.645751311 Reorder the terms: -1 + g = -2.645751311 Solving -1 + g = -2.645751311 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + g = -2.645751311 + 1 Combine like terms: -1 + 1 = 0 0 + g = -2.645751311 + 1 g = -2.645751311 + 1 Combine like terms: -2.645751311 + 1 = -1.645751311 g = -1.645751311 Simplifying g = -1.645751311Solution
The solution to the problem is based on the solutions from the subproblems. g = {3.645751311, -1.645751311}
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