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Simplifying g2 + -10g + 17 = 0 Reorder the terms: 17 + -10g + g2 = 0 Solving 17 + -10g + g2 = 0 Solving for variable 'g'. Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + -10g + -17 + g2 = 0 + -17 Reorder the terms: 17 + -17 + -10g + g2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -10g + g2 = 0 + -17 -10g + g2 = 0 + -17 Combine like terms: 0 + -17 = -17 -10g + g2 = -17 The g term is -10g. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10g + 25 + g2 = -17 + 25 Reorder the terms: 25 + -10g + g2 = -17 + 25 Combine like terms: -17 + 25 = 8 25 + -10g + g2 = 8 Factor a perfect square on the left side: (g + -5)(g + -5) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (g + -5) equal to 2.828427125 and -2.828427125.Subproblem 1
g + -5 = 2.828427125 Simplifying g + -5 = 2.828427125 Reorder the terms: -5 + g = 2.828427125 Solving -5 + g = 2.828427125 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + g = 2.828427125 + 5 Combine like terms: -5 + 5 = 0 0 + g = 2.828427125 + 5 g = 2.828427125 + 5 Combine like terms: 2.828427125 + 5 = 7.828427125 g = 7.828427125 Simplifying g = 7.828427125Subproblem 2
g + -5 = -2.828427125 Simplifying g + -5 = -2.828427125 Reorder the terms: -5 + g = -2.828427125 Solving -5 + g = -2.828427125 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + g = -2.828427125 + 5 Combine like terms: -5 + 5 = 0 0 + g = -2.828427125 + 5 g = -2.828427125 + 5 Combine like terms: -2.828427125 + 5 = 2.171572875 g = 2.171572875 Simplifying g = 2.171572875Solution
The solution to the problem is based on the solutions from the subproblems. g = {7.828427125, 2.171572875}
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