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Simplifying x2 + 54x + 727 = 0 Reorder the terms: 727 + 54x + x2 = 0 Solving 727 + 54x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-727' to each side of the equation. 727 + 54x + -727 + x2 = 0 + -727 Reorder the terms: 727 + -727 + 54x + x2 = 0 + -727 Combine like terms: 727 + -727 = 0 0 + 54x + x2 = 0 + -727 54x + x2 = 0 + -727 Combine like terms: 0 + -727 = -727 54x + x2 = -727 The x term is 54x. Take half its coefficient (27). Square it (729) and add it to both sides. Add '729' to each side of the equation. 54x + 729 + x2 = -727 + 729 Reorder the terms: 729 + 54x + x2 = -727 + 729 Combine like terms: -727 + 729 = 2 729 + 54x + x2 = 2 Factor a perfect square on the left side: (x + 27)(x + 27) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + 27) equal to 1.414213562 and -1.414213562.Subproblem 1
x + 27 = 1.414213562 Simplifying x + 27 = 1.414213562 Reorder the terms: 27 + x = 1.414213562 Solving 27 + x = 1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + x = 1.414213562 + -27 Combine like terms: 27 + -27 = 0 0 + x = 1.414213562 + -27 x = 1.414213562 + -27 Combine like terms: 1.414213562 + -27 = -25.585786438 x = -25.585786438 Simplifying x = -25.585786438Subproblem 2
x + 27 = -1.414213562 Simplifying x + 27 = -1.414213562 Reorder the terms: 27 + x = -1.414213562 Solving 27 + x = -1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + x = -1.414213562 + -27 Combine like terms: 27 + -27 = 0 0 + x = -1.414213562 + -27 x = -1.414213562 + -27 Combine like terms: -1.414213562 + -27 = -28.414213562 x = -28.414213562 Simplifying x = -28.414213562Solution
The solution to the problem is based on the solutions from the subproblems. x = {-25.585786438, -28.414213562}
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