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Simplifying x2 + 31x + 5 = 0 Reorder the terms: 5 + 31x + x2 = 0 Solving 5 + 31x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 31x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 31x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 31x + x2 = 0 + -5 31x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 31x + x2 = -5 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 = -5 + 240.25 Reorder the terms: 240.25 + 31x + x2 = -5 + 240.25 Combine like terms: -5 + 240.25 = 235.25 240.25 + 31x + x2 = 235.25 Factor a perfect square on the left side: (x + 15.5)(x + 15.5) = 235.25 Calculate the square root of the right side: 15.33786165 Break this problem into two subproblems by setting (x + 15.5) equal to 15.33786165 and -15.33786165.Subproblem 1
x + 15.5 = 15.33786165 Simplifying x + 15.5 = 15.33786165 Reorder the terms: 15.5 + x = 15.33786165 Solving 15.5 + x = 15.33786165 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 = 15.33786165 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + x = 15.33786165 + -15.5 x = 15.33786165 + -15.5 Combine like terms: 15.33786165 + -15.5 = -0.16213835 x = -0.16213835 Simplifying x = -0.16213835Subproblem 2
x + 15.5 = -15.33786165 Simplifying x + 15.5 = -15.33786165 Reorder the terms: 15.5 + x = -15.33786165 Solving 15.5 + x = -15.33786165 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 = -15.33786165 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + x = -15.33786165 + -15.5 x = -15.33786165 + -15.5 Combine like terms: -15.33786165 + -15.5 = -30.83786165 x = -30.83786165 Simplifying x = -30.83786165Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.16213835, -30.83786165}
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