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Simplifying x2 + 27x + 31 = 0 Reorder the terms: 31 + 27x + x2 = 0 Solving 31 + 27x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-31' to each side of the equation. 31 + 27x + -31 + x2 = 0 + -31 Reorder the terms: 31 + -31 + 27x + x2 = 0 + -31 Combine like terms: 31 + -31 = 0 0 + 27x + x2 = 0 + -31 27x + x2 = 0 + -31 Combine like terms: 0 + -31 = -31 27x + x2 = -31 The x term is 27x. Take half its coefficient (13.5). Square it (182.25) and add it to both sides. Add '182.25' to each side of the equation. 27x + 182.25 + x2 = -31 + 182.25 Reorder the terms: 182.25 + 27x + x2 = -31 + 182.25 Combine like terms: -31 + 182.25 = 151.25 182.25 + 27x + x2 = 151.25 Factor a perfect square on the left side: (x + 13.5)(x + 13.5) = 151.25 Calculate the square root of the right side: 12.298373876 Break this problem into two subproblems by setting (x + 13.5) equal to 12.298373876 and -12.298373876.Subproblem 1
x + 13.5 = 12.298373876 Simplifying x + 13.5 = 12.298373876 Reorder the terms: 13.5 + x = 12.298373876 Solving 13.5 + x = 12.298373876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.5' to each side of the equation. 13.5 + -13.5 + x = 12.298373876 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = 12.298373876 + -13.5 x = 12.298373876 + -13.5 Combine like terms: 12.298373876 + -13.5 = -1.201626124 x = -1.201626124 Simplifying x = -1.201626124Subproblem 2
x + 13.5 = -12.298373876 Simplifying x + 13.5 = -12.298373876 Reorder the terms: 13.5 + x = -12.298373876 Solving 13.5 + x = -12.298373876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.5' to each side of the equation. 13.5 + -13.5 + x = -12.298373876 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = -12.298373876 + -13.5 x = -12.298373876 + -13.5 Combine like terms: -12.298373876 + -13.5 = -25.798373876 x = -25.798373876 Simplifying x = -25.798373876Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.201626124, -25.798373876}
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