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Simplifying x2 + 31x + 59 = 0 Reorder the terms: 59 + 31x + x2 = 0 Solving 59 + 31x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-59' to each side of the equation. 59 + 31x + -59 + x2 = 0 + -59 Reorder the terms: 59 + -59 + 31x + x2 = 0 + -59 Combine like terms: 59 + -59 = 0 0 + 31x + x2 = 0 + -59 31x + x2 = 0 + -59 Combine like terms: 0 + -59 = -59 31x + x2 = -59 The x term is 31x. Take half its coefficient (15.5). Square it (240.25) and add it to both sides. Add '240.25' to each side of the equation. 31x + 240.25 + x2 = -59 + 240.25 Reorder the terms: 240.25 + 31x + x2 = -59 + 240.25 Combine like terms: -59 + 240.25 = 181.25 240.25 + 31x + x2 = 181.25 Factor a perfect square on the left side: (x + 15.5)(x + 15.5) = 181.25 Calculate the square root of the right side: 13.462912018 Break this problem into two subproblems by setting (x + 15.5) equal to 13.462912018 and -13.462912018.Subproblem 1
x + 15.5 = 13.462912018 Simplifying x + 15.5 = 13.462912018 Reorder the terms: 15.5 + x = 13.462912018 Solving 15.5 + x = 13.462912018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15.5' to each side of the equation. 15.5 + -15.5 + x = 13.462912018 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + x = 13.462912018 + -15.5 x = 13.462912018 + -15.5 Combine like terms: 13.462912018 + -15.5 = -2.037087982 x = -2.037087982 Simplifying x = -2.037087982Subproblem 2
x + 15.5 = -13.462912018 Simplifying x + 15.5 = -13.462912018 Reorder the terms: 15.5 + x = -13.462912018 Solving 15.5 + x = -13.462912018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15.5' to each side of the equation. 15.5 + -15.5 + x = -13.462912018 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + x = -13.462912018 + -15.5 x = -13.462912018 + -15.5 Combine like terms: -13.462912018 + -15.5 = -28.962912018 x = -28.962912018 Simplifying x = -28.962912018Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.037087982, -28.962912018}
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