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Simplifying 17g2 + -92g + -206 = 0 Reorder the terms: -206 + -92g + 17g2 = 0 Solving -206 + -92g + 17g2 = 0 Solving for variable 'g'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -12.11764706 + -5.411764706g + g2 = 0 Move the constant term to the right: Add '12.11764706' to each side of the equation. -12.11764706 + -5.411764706g + 12.11764706 + g2 = 0 + 12.11764706 Reorder the terms: -12.11764706 + 12.11764706 + -5.411764706g + g2 = 0 + 12.11764706 Combine like terms: -12.11764706 + 12.11764706 = 0.00000000 0.00000000 + -5.411764706g + g2 = 0 + 12.11764706 -5.411764706g + g2 = 0 + 12.11764706 Combine like terms: 0 + 12.11764706 = 12.11764706 -5.411764706g + g2 = 12.11764706 The g term is -5.411764706g. Take half its coefficient (-2.705882353). Square it (7.321799308) and add it to both sides. Add '7.321799308' to each side of the equation. -5.411764706g + 7.321799308 + g2 = 12.11764706 + 7.321799308 Reorder the terms: 7.321799308 + -5.411764706g + g2 = 12.11764706 + 7.321799308 Combine like terms: 12.11764706 + 7.321799308 = 19.439446368 7.321799308 + -5.411764706g + g2 = 19.439446368 Factor a perfect square on the left side: (g + -2.705882353)(g + -2.705882353) = 19.439446368 Calculate the square root of the right side: 4.409018753 Break this problem into two subproblems by setting (g + -2.705882353) equal to 4.409018753 and -4.409018753.Subproblem 1
g + -2.705882353 = 4.409018753 Simplifying g + -2.705882353 = 4.409018753 Reorder the terms: -2.705882353 + g = 4.409018753 Solving -2.705882353 + g = 4.409018753 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '2.705882353' to each side of the equation. -2.705882353 + 2.705882353 + g = 4.409018753 + 2.705882353 Combine like terms: -2.705882353 + 2.705882353 = 0.000000000 0.000000000 + g = 4.409018753 + 2.705882353 g = 4.409018753 + 2.705882353 Combine like terms: 4.409018753 + 2.705882353 = 7.114901106 g = 7.114901106 Simplifying g = 7.114901106Subproblem 2
g + -2.705882353 = -4.409018753 Simplifying g + -2.705882353 = -4.409018753 Reorder the terms: -2.705882353 + g = -4.409018753 Solving -2.705882353 + g = -4.409018753 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '2.705882353' to each side of the equation. -2.705882353 + 2.705882353 + g = -4.409018753 + 2.705882353 Combine like terms: -2.705882353 + 2.705882353 = 0.000000000 0.000000000 + g = -4.409018753 + 2.705882353 g = -4.409018753 + 2.705882353 Combine like terms: -4.409018753 + 2.705882353 = -1.7031364 g = -1.7031364 Simplifying g = -1.7031364Solution
The solution to the problem is based on the solutions from the subproblems. g = {7.114901106, -1.7031364}
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