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Simplifying x2 + 17x + -109 = 0 Reorder the terms: -109 + 17x + x2 = 0 Solving -109 + 17x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '109' to each side of the equation. -109 + 17x + 109 + x2 = 0 + 109 Reorder the terms: -109 + 109 + 17x + x2 = 0 + 109 Combine like terms: -109 + 109 = 0 0 + 17x + x2 = 0 + 109 17x + x2 = 0 + 109 Combine like terms: 0 + 109 = 109 17x + x2 = 109 The x term is 17x. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17x + 72.25 + x2 = 109 + 72.25 Reorder the terms: 72.25 + 17x + x2 = 109 + 72.25 Combine like terms: 109 + 72.25 = 181.25 72.25 + 17x + x2 = 181.25 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 181.25 Calculate the square root of the right side: 13.462912018 Break this problem into two subproblems by setting (x + 8.5) equal to 13.462912018 and -13.462912018.Subproblem 1
x + 8.5 = 13.462912018 Simplifying x + 8.5 = 13.462912018 Reorder the terms: 8.5 + x = 13.462912018 Solving 8.5 + x = 13.462912018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = 13.462912018 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 13.462912018 + -8.5 x = 13.462912018 + -8.5 Combine like terms: 13.462912018 + -8.5 = 4.962912018 x = 4.962912018 Simplifying x = 4.962912018Subproblem 2
x + 8.5 = -13.462912018 Simplifying x + 8.5 = -13.462912018 Reorder the terms: 8.5 + x = -13.462912018 Solving 8.5 + x = -13.462912018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = -13.462912018 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -13.462912018 + -8.5 x = -13.462912018 + -8.5 Combine like terms: -13.462912018 + -8.5 = -21.962912018 x = -21.962912018 Simplifying x = -21.962912018Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.962912018, -21.962912018}
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