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Simplifying x2 + 27x + 138 = 0 Reorder the terms: 138 + 27x + x2 = 0 Solving 138 + 27x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-138' to each side of the equation. 138 + 27x + -138 + x2 = 0 + -138 Reorder the terms: 138 + -138 + 27x + x2 = 0 + -138 Combine like terms: 138 + -138 = 0 0 + 27x + x2 = 0 + -138 27x + x2 = 0 + -138 Combine like terms: 0 + -138 = -138 27x + x2 = -138 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 = -138 + 182.25 Reorder the terms: 182.25 + 27x + x2 = -138 + 182.25 Combine like terms: -138 + 182.25 = 44.25 182.25 + 27x + x2 = 44.25 Factor a perfect square on the left side: (x + 13.5)(x + 13.5) = 44.25 Calculate the square root of the right side: 6.652067348 Break this problem into two subproblems by setting (x + 13.5) equal to 6.652067348 and -6.652067348.Subproblem 1
x + 13.5 = 6.652067348 Simplifying x + 13.5 = 6.652067348 Reorder the terms: 13.5 + x = 6.652067348 Solving 13.5 + x = 6.652067348 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 = 6.652067348 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = 6.652067348 + -13.5 x = 6.652067348 + -13.5 Combine like terms: 6.652067348 + -13.5 = -6.847932652 x = -6.847932652 Simplifying x = -6.847932652Subproblem 2
x + 13.5 = -6.652067348 Simplifying x + 13.5 = -6.652067348 Reorder the terms: 13.5 + x = -6.652067348 Solving 13.5 + x = -6.652067348 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 = -6.652067348 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = -6.652067348 + -13.5 x = -6.652067348 + -13.5 Combine like terms: -6.652067348 + -13.5 = -20.152067348 x = -20.152067348 Simplifying x = -20.152067348Solution
The solution to the problem is based on the solutions from the subproblems. x = {-6.847932652, -20.152067348}
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