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Simplifying x2 + 29x + 29 = 0 Reorder the terms: 29 + 29x + x2 = 0 Solving 29 + 29x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-29' to each side of the equation. 29 + 29x + -29 + x2 = 0 + -29 Reorder the terms: 29 + -29 + 29x + x2 = 0 + -29 Combine like terms: 29 + -29 = 0 0 + 29x + x2 = 0 + -29 29x + x2 = 0 + -29 Combine like terms: 0 + -29 = -29 29x + x2 = -29 The x term is 29x. Take half its coefficient (14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. 29x + 210.25 + x2 = -29 + 210.25 Reorder the terms: 210.25 + 29x + x2 = -29 + 210.25 Combine like terms: -29 + 210.25 = 181.25 210.25 + 29x + x2 = 181.25 Factor a perfect square on the left side: (x + 14.5)(x + 14.5) = 181.25 Calculate the square root of the right side: 13.462912018 Break this problem into two subproblems by setting (x + 14.5) equal to 13.462912018 and -13.462912018.Subproblem 1
x + 14.5 = 13.462912018 Simplifying x + 14.5 = 13.462912018 Reorder the terms: 14.5 + x = 13.462912018 Solving 14.5 + x = 13.462912018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + x = 13.462912018 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x = 13.462912018 + -14.5 x = 13.462912018 + -14.5 Combine like terms: 13.462912018 + -14.5 = -1.037087982 x = -1.037087982 Simplifying x = -1.037087982Subproblem 2
x + 14.5 = -13.462912018 Simplifying x + 14.5 = -13.462912018 Reorder the terms: 14.5 + x = -13.462912018 Solving 14.5 + x = -13.462912018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + x = -13.462912018 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x = -13.462912018 + -14.5 x = -13.462912018 + -14.5 Combine like terms: -13.462912018 + -14.5 = -27.962912018 x = -27.962912018 Simplifying x = -27.962912018Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.037087982, -27.962912018}
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